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BEGIN:VEVENT
SUMMARY:Yoshinori Gongyo (The University of Tokyo)
DTSTART;VALUE=DATE-TIME:20200423T160000Z
DTEND;VALUE=DATE-TIME:20200423T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/1
DESCRIPTION:Title: On a
generalized Batyrev's cone conjecture\nby Yoshinori Gongyo (The Unive
rsity of Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/ZAG/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Hacon (The University of Utah)
DTSTART;VALUE=DATE-TIME:20200428T160000Z
DTEND;VALUE=DATE-TIME:20200428T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/2
DESCRIPTION:Title: Rece
nt progress in the MMP for 3-folds and 4-folds in char p>0\nby Christo
pher Hacon (The University of Utah) as part of ZAG (Zoom Algebraic Geometr
y) seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ZAG/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arnaud Beauville (Université de Nice)
DTSTART;VALUE=DATE-TIME:20200430T150000Z
DTEND;VALUE=DATE-TIME:20200430T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/3
DESCRIPTION:Title: Vect
or bundles on Fano threefolds and K3 surfaces\nby Arnaud Beauville (Un
iversité de Nice) as part of ZAG (Zoom Algebraic Geometry) seminar\n\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/ZAG/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chen Jiang (Shanghai Center for Mathematical Sciences\, Fudan Univ
ersity)
DTSTART;VALUE=DATE-TIME:20200505T150000Z
DTEND;VALUE=DATE-TIME:20200505T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/4
DESCRIPTION:Title: Mini
mal log discrepancies of 3-dimensional non-canonical singularities\nby
Chen Jiang (Shanghai Center for Mathematical Sciences\, Fudan University)
as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nCanonical
and terminal singularities\, introduced by Reid\, appear naturally in min
imal model program and play important roles in the birational classificati
on of higher dimensional algebraic varieties. Such singularities are well-
understood in dimension 3\, while the property of non-canonical singularit
ies is still mysterious. We investigate the difference between canonical a
nd non-canonical singularities via minimal log discrepancies (MLD). We sho
w that there is a gap between MLD of 3-dimensional non-canonical singulari
ties and that of 3-dimensional canonical singularities\, which is predicte
d by a conjecture of Shokurov. This result on local singularities has appl
ications to global geometry of Calabi–Yau 3-folds. We show that the set
of all non-canonical klt Calabi–Yau 3-folds are bounded modulo flops\, a
nd the global indices of all klt Calabi–Yau 3-folds are bounded from abo
ve.\n
LOCATION:https://researchseminars.org/talk/ZAG/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Grushevsky (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20200507T180000Z
DTEND;VALUE=DATE-TIME:20200507T190000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/5
DESCRIPTION:Title: Geom
etry of moduli of cubic threefolds\nby Samuel Grushevsky (Stony Brook
University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract
\nThe moduli space of cubic threefolds can be thought of as a GIT quotient
of the projective space of all cubic polynomials\, studied via the period
map to a ball quotient\, or via the intermediate Jacobians. We describe t
he relations between various compactifications of the moduli space of cubi
c threefolds that arise in these ways\, and compute their cohomology. Base
d on joint works with S. Casalaina-Martin\, K. Hulek\, R. Laza.\n
LOCATION:https://researchseminars.org/talk/ZAG/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristin De Vleming (University of California\, San Diego)
DTSTART;VALUE=DATE-TIME:20200512T160000Z
DTEND;VALUE=DATE-TIME:20200512T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/6
DESCRIPTION:Title: Wall
crossing for K-moduli spaces of plane curves\nby Kristin De Vleming (
University of California\, San Diego) as part of ZAG (Zoom Algebraic Geome
try) seminar\n\n\nAbstract\nThis talk will focus on compactifications of t
he moduli space of smooth plane curves of degree d at least 4. We will re
gard a plane curve as a log Fano pair (P2\, aC)\, where a is a rational nu
mber\, and study the compactifications arising from K stability for these
pairs and log Fano pairs in general. We establish a wall crossing framewo
rk to study these spaces as a varies and show that\, when a is small\, the
moduli space coming from K stability is isomorphic to the GIT moduli spac
e. We describe all wall crossings for degree 4\, 5\, and 6 plane curves a
nd discuss the picture for general Q-Gorenstein smoothable log Fano pairs.
This is joint work with Kenneth Ascher and Yuchen Liu.\n
LOCATION:https://researchseminars.org/talk/ZAG/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Christian Ottem (University of Oslo)
DTSTART;VALUE=DATE-TIME:20200514T153000Z
DTEND;VALUE=DATE-TIME:20200514T163000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/7
DESCRIPTION:Title: Trop
ical degenerations and stable rationality\nby John Christian Ottem (Un
iversity of Oslo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/ZAG/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mircea Mustață (University of Michigan)
DTSTART;VALUE=DATE-TIME:20200519T170000Z
DTEND;VALUE=DATE-TIME:20200519T180000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/11
DESCRIPTION:Title: Min
imal exponent and Hodge filtrations\nby Mircea Mustață (University o
f Michigan) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract
\nI will discuss an invariant of singularities\, Saito's minimal exponent\
, and its connections with various other invariants of singularities. The
minimal exponent is a refinement of the log canonical threshold that can b
e used to also measure rational hypersurface singularities. This is based
on joint work with Mihnea Popa.\n
LOCATION:https://researchseminars.org/talk/ZAG/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zsolt Patakfalvi (École polytechnique fédérale de Lausanne)
DTSTART;VALUE=DATE-TIME:20200526T170000Z
DTEND;VALUE=DATE-TIME:20200526T180000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/12
DESCRIPTION:Title: On
the Beauville-Bogomolov decomposition in positive characteristic\nby Z
solt Patakfalvi (École polytechnique fédérale de Lausanne) as part of Z
AG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAbstract: I will pres
ent a joint with Maciej Zdanowicz towards a positive characteristic versio
n of the Beauville-Bogomolov decomposition. Over the complex numbers this
decomposition was shown using differential geometry methods in the 70's an
d in the 80's. It concerns varieties with trivial canonical bundle\, which
we call K-trivial here. The main statement over the complex number is tha
t smooth projective K-trivial varieties admit an etale cover which splits
as a product of three types of varieties: abelian\, Calabi-Yau and symplec
tic. I will present a similar statement in positive characteristic for (we
akly) ordinary K-trivial varieties\, the proof of which uses purely positi
ve characteristic methods.\n
LOCATION:https://researchseminars.org/talk/ZAG/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xavier Roulleau (University of Aix-Marseille)
DTSTART;VALUE=DATE-TIME:20200521T110000Z
DTEND;VALUE=DATE-TIME:20200521T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/13
DESCRIPTION:Title: On
the geometric models of K3 surfaces with finite automorphism group and Pic
ard number larger than two\nby Xavier Roulleau (University of Aix-Mars
eille) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nVin
berg and Nikulin classified K3 surfaces which have finite automorphism gro
up and Picard number 4 and 3\,5\,..\,19 respectively. That classification
is lattice theoretic\, according to the Neron-Severi group of these surfac
es\; there are 118 such lattices. In this talk I will discuss on the geome
tric construction of these surfaces (by double coverings or complete inter
sections) and describe their (finite) set of (-2)-curves\, which gives the
ample cone. Most of the moduli spaces of these K3 surfaces are unirationa
l. A part of this talk is based on a joint work with Michela Artebani and
Claudia Correa Diesler.\n
LOCATION:https://researchseminars.org/talk/ZAG/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Kuznetsova (Higher School of Economics)
DTSTART;VALUE=DATE-TIME:20200528T140000Z
DTEND;VALUE=DATE-TIME:20200528T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/18
DESCRIPTION:Title: Sex
tic double solids\nby Alexandra Kuznetsova (Higher School of Economics
) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAbstract
: One of the first examples of unirational non-rational threefold was prov
ided by Artin and Mumford and it was a double cover of P^3 branched in a n
odal quartic surface\, so called quartic double solid.\nThen Endrass studi
ed this class of varieties and showed that the example by Artin and Mumfor
d gives a unique family of non-rational nodal quartic double solids. I am
going to tell about the next interesting class of threefolds --- nodal sex
tic double solids. I will describe 4 families of them such that any non-ra
tional variety of this type lies in one of those families and explain the
proof.\n
LOCATION:https://researchseminars.org/talk/ZAG/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Schreieder (Leibniz University)
DTSTART;VALUE=DATE-TIME:20200602T110000Z
DTEND;VALUE=DATE-TIME:20200602T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/19
DESCRIPTION:Title: Equ
ality in the Bogomolov-Miyaoka-Yau inequality in the non-general type case
\nby Stefan Schreieder (Leibniz University) as part of ZAG (Zoom Algeb
raic Geometry) seminar\n\n\nAbstract\nWe classify all good minimal models
of dimension n and with vanishing Chern number $c_1^{n-2}c_2(X)=0$\, which
corresponds to equality in the Bogomolov-Miyaoka—Yau inequality in the
non-general type case. Here the most interesting case is that of Kodaira d
imension n-1\, where any minimal model is known to be good. Our result sol
ves completely a problem a Kollar. In dimension three\, our approach toget
her with previous work of Grassi and Kollar also leads to a complete solut
ion of a conjecture of Kollar\, asserting that on a minimal threefold\, c_
1c_2 is either zero or universally bounded away from zero. Joint work with
Feng Hao.\n
LOCATION:https://researchseminars.org/talk/ZAG/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caucher Birkar (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20200604T130000Z
DTEND;VALUE=DATE-TIME:20200604T140000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/20
DESCRIPTION:Title: Geo
metry of polarised varieties\nby Caucher Birkar (University of Cambrid
ge) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will
talk about projective varieties polarised by ample divisors (or more gene
rally nef and big divisors) in particular from a birational geometry point
of view\, and present some recent results in this direction.\n
LOCATION:https://researchseminars.org/talk/ZAG/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Prokhorov (Moscow State University)
DTSTART;VALUE=DATE-TIME:20200609T153000Z
DTEND;VALUE=DATE-TIME:20200609T163000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/21
DESCRIPTION:Title: Gen
eral elephants for 3-fold extremal contractions\nby Yuri Prokhorov (Mo
scow State University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\
n\nAbstract\nI will discuss effective results on the classification of ext
remal contractions in the 3-dimensional MMP. In particular\, I will presen
t some recent result based on joint work with Shigefumi Mori on the existe
nce of general elephants.\n
LOCATION:https://researchseminars.org/talk/ZAG/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Zharkov (Kansas State University)
DTSTART;VALUE=DATE-TIME:20200611T140000Z
DTEND;VALUE=DATE-TIME:20200611T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/22
DESCRIPTION:Title: Top
ological SYZ fibrations with discriminant in codimension 2\nby Ilya Zh
arkov (Kansas State University) as part of ZAG (Zoom Algebraic Geometry) s
eminar\n\n\nAbstract\nTo date only for K3 surfaces (trivial) and the quint
ic threefold (due to M. Gross) the discriminant can be made to be in codim
ension two. I will outline the source of the problem and how to resolve it
in much more general situations using phase and over-tropical pairs-of-pa
nts. Joint project with Helge Ruddat.\n
LOCATION:https://researchseminars.org/talk/ZAG/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolaos Tziolas (University of Cyprus)
DTSTART;VALUE=DATE-TIME:20200616T153000Z
DTEND;VALUE=DATE-TIME:20200616T163000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/23
DESCRIPTION:Title: Vec
tor fields on canonically polarized surfaces\nby Nikolaos Tziolas (Uni
versity of Cyprus) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA
bstract\nIn this talk I will present some results about the geometry of c
anonically polarized surfaces defined over a field of positive characteris
tic which have a nontrivial global vector field\, equivalently non reduced
automorphism scheme\, and the implications that the existence of such sur
faces has in the moduli problem of canonically polarized surfaces.\n
LOCATION:https://researchseminars.org/talk/ZAG/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claire Voisin (Collège de France)
DTSTART;VALUE=DATE-TIME:20200618T140000Z
DTEND;VALUE=DATE-TIME:20200618T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/24
DESCRIPTION:Title: Tri
angle varieties and surface decomposition of hyper-Kahler manifolds\nb
y Claire Voisin (Collège de France) as part of ZAG (Zoom Algebraic Geomet
ry) seminar\n\n\nAbstract\nIn recent years\, new constructions of complete
families of polarized hyper-Kahler manifolds have been found starting fro
m Fano geometry. These hyper-Kahler manifolds also appear as general defor
mations of Hilbert schemes of K3 surfaces or O'Grady manifolds. I will int
roduce the notion of surface decomposition for a variety X with a nontrivi
al Hodge structure on degree 2 cohomology. I will show that this notion is
restrictive topologically\, as it implies Beauville-Fujiki type relations
. I will also show the existence of such a surface decomposition for the
general hyper-Kahler manifolds mentioned above. This has interesting co
nsequences on Beauville's conjecture on the Chow ring of hyper-Kahler mani
folds.\n
LOCATION:https://researchseminars.org/talk/ZAG/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Polishchuk (University of Oregon)
DTSTART;VALUE=DATE-TIME:20200623T170000Z
DTEND;VALUE=DATE-TIME:20200623T180000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/25
DESCRIPTION:Title: Hyp
erelliptic limits of quadrics through canonical curves and the super-Schot
tky locus\nby Alexander Polishchuk (University of Oregon) as part of Z
AG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will describe joint
works with Eric Rains and with Giovanni Felder and David Kazhdan. The firs
t part will be about a classical topic of quadrics through canonically emb
edded curves. We study limiting quadrics as canonical curves approach a hy
perelliptic limit. There is a surprizingly simple description of all such
limits. I will also discuss the connection to ribbon curves (which are thi
ckenings of rational normal curves) and to the blow up of the moduli space
of curves at the hyperelliptic locus. In the second part I will talk abou
t the super-period map for supercurves and the calculation of its infinite
simal variation. This variation is given by a natural Massey product that
can be defined for any curve with a theta-characteristic. Combining this w
ith the result of part 1 we get some information about the super-Schottky
locus.\n
LOCATION:https://researchseminars.org/talk/ZAG/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Mumford (Harvard University and Brown University)
DTSTART;VALUE=DATE-TIME:20200625T150000Z
DTEND;VALUE=DATE-TIME:20200625T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/26
DESCRIPTION:Title: A m
oduli space in the differential geometry world\nby David Mumford (Harv
ard University and Brown University) as part of ZAG (Zoom Algebraic Geomet
ry) seminar\n\n\nAbstract\nThe space of simple closed smooth plane curves
is an infinite dimensional manifold and supports a great diversity of Riem
annian metrics. They have very diverse curvature properties and even inclu
de universal Teichmuller space. I want to talk in particular about a recen
t example: modeling 2D waves in water (aka gravity waves) that some believ
e explains so-called rogue waves.\nAfter the talk\, we plan to have Q&A se
ssion at 16:00 GMT. If you have a question for Prof. Mumford\, let Ivan Ch
eltsov know in advance (by e-mail).\n
LOCATION:https://researchseminars.org/talk/ZAG/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Izzet Coskun (University of Illinois at Chicago)
DTSTART;VALUE=DATE-TIME:20200630T150000Z
DTEND;VALUE=DATE-TIME:20200630T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/27
DESCRIPTION:Title: The
stabilization of the cohomology of moduli spaces of sheaves on surfaces\nby Izzet Coskun (University of Illinois at Chicago) as part of ZAG (Zo
om Algebraic Geometry) seminar\n\n\nAbstract\nThe Betti numbers of the Hil
bert scheme of points on a smooth\, irreducible projective surface have be
en computed by Gottsche. These numbers stabilize as the number of points t
ends to infinity. In contrast\, the Betti numbers of moduli spaces of semi
stable sheaves on a surface are not known in general. In joint work with M
atthew Woolf\, we conjecture these also stabilize and that the stable numb
ers do not depend on the rank. We verify the conjecture for large classes
of surfaces. I will discuss our conjecture and provide the evidence for it
.\n
LOCATION:https://researchseminars.org/talk/ZAG/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Susanna Zimmermann (Université Angers)
DTSTART;VALUE=DATE-TIME:20200702T100000Z
DTEND;VALUE=DATE-TIME:20200702T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/28
DESCRIPTION:Title: Fin
ite quotients of Cremona groups\nby Susanna Zimmermann (Université An
gers) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nThe
Cremona group is the group of birational self-maps of the projective space
\, and it is very very big. While in dimension 2 over algebraically closed
fields there are no finite quotients of this group\, there are many such
quotients over non-closed fields and in higher dimension. I will discuss w
hy this is and how these quotients come up.\n
LOCATION:https://researchseminars.org/talk/ZAG/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziquan Zhuang (MIT)
DTSTART;VALUE=DATE-TIME:20200707T170000Z
DTEND;VALUE=DATE-TIME:20200707T180000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/29
DESCRIPTION:Title: K-s
tability of Fano varieties via admissible flags\nby Ziquan Zhuang (MIT
) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI'll pre
sent a general approach to prove the K-stability of explicit Fano varietie
s. Among the applications\, we confirm the existence of K\\"ahler-Einstein
metrics on all smooth Fano hypersurfaces of Fano index two\, calculate th
e stability thresholds of some Fano varieties and provide a counterexample
to the Higher Rank Finite Generation conjecture. Based on joint work with
Hamid Ahmadinezhad.\n
LOCATION:https://researchseminars.org/talk/ZAG/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harold Blum (University of Utah)
DTSTART;VALUE=DATE-TIME:20200709T150000Z
DTEND;VALUE=DATE-TIME:20200709T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/30
DESCRIPTION:Title: On
properness of K-moduli spaces and destabilizations of Fano varieties\n
by Harold Blum (University of Utah) as part of ZAG (Zoom Algebraic Geometr
y) seminar\n\n\nAbstract\nK-stability is an algebraic notion that detects
when a smooth Fano variety admits a Kahler-Einstein metric. Recently\, the
re has been significant progress on constructing moduli spaces of K-polyst
able Fano varieties using algebraic methods. One of the remaining open pro
blems is to show that these moduli spaces are proper. In this talk\, I wil
l discuss work with Daniel Halpern-Leistner\, Yuchen Liu\, and Chenyang Xu
\, in which we reduce the properness of such K-moduli spaces to the existe
nce of certain optimal destabilization of Fano varieties.\n
LOCATION:https://researchseminars.org/talk/ZAG/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hélène Esnault (Freie Universität Berlin)
DTSTART;VALUE=DATE-TIME:20200714T140000Z
DTEND;VALUE=DATE-TIME:20200714T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/31
DESCRIPTION:Title: Den
sity of arithmetic representations\nby Hélène Esnault (Freie Univers
ität Berlin) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstra
ct\nThe lecture surveys recent work with Moritz Kerz. The motivation is t
he conjecture that the Hard-Lefschetz (HL) property holds on smooth proje
ctive varieties defined over algebraically closed char. $p>0$ fields for
cohomology with values in semi-simple $\\ell$-adic local systems $V$. We
know it is true if $V$ comes from geometry (Deligne\, Beilinson-Bernstein-
Deligne-Gabber) by Deligne’s theory of weights. In absence of weights\,
we proved it if $V$ has rank $1$ and reduced the whole HL conjecture to a
density conjecture on arithmetic semi-simple $\\ell$-adic systems on $P^1$
minus $3$ closed points\, which we can prove in rank $2$.\n
LOCATION:https://researchseminars.org/talk/ZAG/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Schuett (Leibniz Universität Hannover)
DTSTART;VALUE=DATE-TIME:20200716T153000Z
DTEND;VALUE=DATE-TIME:20200716T163000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/32
DESCRIPTION:Title: Rat
ional curves on Enriques surfaces\, but only few\nby Matthias Schuett
(Leibniz Universität Hannover) as part of ZAG (Zoom Algebraic Geometry) s
eminar\n\n\nAbstract\nRational curves play a fundamental role for the stru
cture of an Enriques surface. I will first review the general theory befor
e focussing on the case of low degree rational curves. To this end\, I wil
l discuss joint work with S. Rams (Krakow) which develops an explicit shar
p bound on the number of rational curves of given degree relative to the d
egree of the surface. The proof builds on a general argument in parallel t
o the case of K3 surfaces which allows us to extend bounds of Miyaoka and
Degtyarev.\n
LOCATION:https://researchseminars.org/talk/ZAG/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jihun Park (POSTECH)
DTSTART;VALUE=DATE-TIME:20200721T110000Z
DTEND;VALUE=DATE-TIME:20200721T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/33
DESCRIPTION:Title: Cay
ley octads\, plane quartic curves\, Del Pezzo surfaces of degree 2 and dou
ble Veronese cones\nby Jihun Park (POSTECH) as part of ZAG (Zoom Algeb
raic Geometry) seminar\n\n\nAbstract\nA net of quadrics in the 3-dimension
al projective space whose singular members are parametrized by a smooth pl
ane quartic curve has exactly eight distinct base points\, called a regula
r Cayley octad. It is a classical result that there is a one-to-one corr
espondence between isomorphism classes of regular Cayley octads and isomor
phism classes of smooth plane quartic curves equipped with even theta-char
acteristics. We can also easily observe a one-to-one correspondence betwe
en isomorphism classes of smooth plane quartic curves and isomorphism clas
ses of smooth Del Pezzo surfaces of degree 2. In this talk\, we set up a o
ne-to-one correspondence between isomorphism classes of smooth plane quart
ic curves and isomorphism classes of double Veronese cones with 28-singula
r points. Also\, we explain how the 36 even theta characteristics of a giv
en smooth quartic curve appear in the corresponding double Veronese cone.
This is a joint work with Hamid Ahmadinezhad\, Ivan Cheltsov and Constanti
n Shramov.\n
LOCATION:https://researchseminars.org/talk/ZAG/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruadhai Dervan (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20200723T150000Z
DTEND;VALUE=DATE-TIME:20200723T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/34
DESCRIPTION:Title: Sta
bility of fibrations\nby Ruadhai Dervan (University of Cambridge) as p
art of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nThe notion of
K-stability of a polarised variety has been heavily studied in recent year
s\, due to its link both with moduli theory (one should be able to form mo
duli spaces of K-stable varieties) and to Kahler geometry (K-stability sho
uld be equivalent to the existence of a constant scalar curvature Kahler m
etric on the variety). This story has been particularly successful for Fan
o varieties. I will describe a notion of stability for polarised fibration
s\, which generalises K-stability of polarised varieties when the base of
the fibration is a point\, and slope stability of a vector bundle when the
variety is the projectivisation of a vector bundle. I will speculate that
one should be able to form moduli spaces of stable fibrations\, much as o
ne can form moduli spaces of slope stable vector bundles over a fixed base
. The main result\, however\, will be a description of the link with certa
in canonical metrics on fibrations. This is joint work with Lars Sektnan.\
n
LOCATION:https://researchseminars.org/talk/ZAG/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Pierre Demailly (Université Grenoble Alpes)
DTSTART;VALUE=DATE-TIME:20200728T153000Z
DTEND;VALUE=DATE-TIME:20200728T163000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/35
DESCRIPTION:Title: Her
mitian-Yang-Mills approach to the conjecture of Griffiths on the positivit
y of ample vector bundles\nby Jean-Pierre Demailly (Université Grenob
le Alpes) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\n
Given a vector bundle of arbitrary rank with ample determinant line bundle
on a projective manifold\, we propose a new elliptic system of differenti
al equations of Hermitian-Yang-Mills type for the curvature tensor. The sy
stem is designed so that solutions provide Hermitian metrics with positive
curvature in the sense of Griffiths - and even in the stronger dual Nakan
o sense. As a consequence\, if an existence result could be obtained for e
very ample vector bundle\, the Griffiths conjecture on the equivalence be
tween ampleness and positivity of vector bundles would be settled. We also
discuss a new concept of volume for vector bundles.\n
LOCATION:https://researchseminars.org/talk/ZAG/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziwen Zhu (University of Utah)
DTSTART;VALUE=DATE-TIME:20200730T150000Z
DTEND;VALUE=DATE-TIME:20200730T163000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/36
DESCRIPTION:Title: Equ
ivariant K-stability under finite group action\nby Ziwen Zhu (Universi
ty of Utah) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract
\nEquivariant K-stability is defined via equivariant test configurations.
By definition it is weaker than the usual K-stability and for varieties wi
th large symmetry\, it is often easier to check equivariant K-stability. F
or reductive group action\, it is conjectured that equivariant K-polystabi
lity implies K-polystability. In this talk\, I will discuss recent results
about equivariant K-stability and present a proof of the conjecture for f
inite group action. The talk is based on joint work with Yuchen Liu.\n
LOCATION:https://researchseminars.org/talk/ZAG/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamid Ahmadinezhad (Loughborough University)
DTSTART;VALUE=DATE-TIME:20200804T140000Z
DTEND;VALUE=DATE-TIME:20200804T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/37
DESCRIPTION:Title: Bir
ational geometry of Fano 3-fold hypersurfaces of higher index\nby Hami
d Ahmadinezhad (Loughborough University) as part of ZAG (Zoom Algebraic Ge
ometry) seminar\n\n\nAbstract\nI will speak about an approach to birationa
l classification of Fano 3-folds\, post MMP. As a part of this general gui
deline\, I will highlight some recent results about birational geometry of
Fano hypersurfaces of higher index. The latter is a joint work with Ivan
Cheltsov and Jihun Park.\n
LOCATION:https://researchseminars.org/talk/ZAG/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Logares (Universidad Complutense de Madrid)
DTSTART;VALUE=DATE-TIME:20200806T150000Z
DTEND;VALUE=DATE-TIME:20200806T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/38
DESCRIPTION:Title: Poi
sson and symplectic geometry of the moduli spaces of Higgs bundles\nby
Marina Logares (Universidad Complutense de Madrid) as part of ZAG (Zoom A
lgebraic Geometry) seminar\n\n\nAbstract\nI will talk about some natural P
oisson and symplectic properties of the moduli spaces of Higgs bundles whe
n some extra structure\, such as a framing\, is added. This is an overview
of various past and ongoing work with I. Biswas\, J. Martens\, A. Peón-N
ieto and S. Szabó. I will not assume any previous knowledge on the subjec
t.\n
LOCATION:https://researchseminars.org/talk/ZAG/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Lazarsfeld (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20200811T170000Z
DTEND;VALUE=DATE-TIME:20200811T180000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/39
DESCRIPTION:Title: Cay
ley-Bacharach theorems and multiplier ideals\nby Robert Lazarsfeld (St
ony Brook University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n
\nAbstract\nCayley-Bacharach theorems originate in the classical statement
if two plane curves of degrees c and d meet in cd points\, then any cur
ve of degree (c + d - 3) passing through all but one of these points must
also pass through the remaining one. Following work of Griffiths and Harri
s in the 1970s\, one now sees this as a special case of a general result a
bout zero-loci of sections of a vector bundle. I will explain how bringing
multiplier ideals into the picture leads (for free) to a variant that all
ows for excess vanishing. This is joint work with Lawrence Ein.\n
LOCATION:https://researchseminars.org/talk/ZAG/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuchen Liu (Yale University)
DTSTART;VALUE=DATE-TIME:20200813T150000Z
DTEND;VALUE=DATE-TIME:20200813T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/40
DESCRIPTION:Title: On
K-stability of cubic hypersurfaces\nby Yuchen Liu (Yale University) as
part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nK-stability
of Fano varieties is an algebro-geometric stability condition characterizi
ng the existence of K\\"ahler-Einstein metrics. Recent progress on K-stabi
lity suggests that it provides a good moduli theory for Fano varieties. In
this talk\, I will explain how K-moduli spaces can help us prove K-stabil
ity of smooth cubic hypersurfaces in dimension at most 4\, using a local-t
o-global volume comparison result. Part of this talk is based on joint wor
k with Chenyang Xu.\n
LOCATION:https://researchseminars.org/talk/ZAG/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Corti (Imperial College London)
DTSTART;VALUE=DATE-TIME:20200818T170000Z
DTEND;VALUE=DATE-TIME:20200818T180000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/41
DESCRIPTION:Title: Smo
othing Gorenstein toric affine 3-folds\nby Alessio Corti (Imperial Co
llege London) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstra
ct\nI will state a conjecture on the smoothing components of the deformati
on space\, and discuss one or more of the following topics: possible strat
egies for proving it\, applications to the Fanosearch program\, global and
higher dimensional analogs. The talk is based on a recent collaboration w
ith Andrea Petracci and Matej Filip.\n
LOCATION:https://researchseminars.org/talk/ZAG/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Pagani (University of Liverpool)
DTSTART;VALUE=DATE-TIME:20200820T150000Z
DTEND;VALUE=DATE-TIME:20200820T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/42
DESCRIPTION:Title: Cla
ssifying fine compactified universal Jacobians\nby Nicola Pagani (Univ
ersity of Liverpool) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\
nAbstract\nWe introduce the notion of a fine compactified Jacobian of a no
dal curve\, as an arbitrary compact open subspace of the moduli space of r
ank-1 torsion-free simple sheaves. We show that fine compactified Jacobian
s correspond to a certain combinatorial datum\, which is obtained by only
keeping track\, for all sheaves\, of (1) the locus where it fails to be lo
cally free\, and (2) its multidegree. This notion generalizes to flat fami
lies of curves\, and so does its combinatorial counterpart. When the famil
y is the universal family over the moduli space of curves\, we have the fo
llowing results: (a) in the absence of marked points\, we can fully classi
fy these combinatorial data and deduce that the only fine compactified uni
versal Jacobians are the classical ones (which were constructed by Pandhar
ipande and Simpson in the nineties) and (b) in the presence of marked poin
ts there are exotic (and new) examples that cannot be obtained as compacti
fied universal Jacobians associated to a polarization. This is a joint wor
k in progress with Jesse Kass.\n
LOCATION:https://researchseminars.org/talk/ZAG/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Boehning (University of Warwick)
DTSTART;VALUE=DATE-TIME:20200825T170000Z
DTEND;VALUE=DATE-TIME:20200825T180000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/43
DESCRIPTION:Title: Rig
id\, not infinitesimally rigid surfaces of general type with ample canonic
al bundle\nby Christian Boehning (University of Warwick) as part of ZA
G (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn the talk I will repo
rt on work in progress\, joint with Roberto Pignatelli and Hans-Christian
von Bothmer\, that concerns the construction of surfaces of general type w
ith ample canonical bundle and Kuranishi space (and possibly also Gieseker
moduli space) a non-reduced point. The main tools are configurations of l
ines and their incidence schemes as well as the theory of abelian covers d
ue to Pardini and others.\n
LOCATION:https://researchseminars.org/talk/ZAG/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Berman (Chalmers University of Technology)
DTSTART;VALUE=DATE-TIME:20200827T100000Z
DTEND;VALUE=DATE-TIME:20200827T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/44
DESCRIPTION:Title: Kah
ler-Einstein metrics\, Archimedean Zeta functions and phase transitions\nby Robert Berman (Chalmers University of Technology) as part of ZAG (Zo
om Algebraic Geometry) seminar\n\n\nAbstract\nWhile the existence of a uni
que Kahler-Einstein metrics on a canonically polarized manifold X was esta
blished already in the seventies there are very few explicit formulas avai
lable (even in the case of complex curves!). In this talk I will give a no
n-technical introduction to a probabilistic approach to Kahler-Einstein me
trics\, which\, in particular\, yields canonical approximations of the Kah
ler-Einstein metric on X. The approximating metrics in question are expres
sed as explicit period integrals and the conjectural extension to the case
of a Fano variety leads to some intriguing connections with Zeta function
s and the theory of phase transitions in statistical mechanics.\n
LOCATION:https://researchseminars.org/talk/ZAG/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jarod Alper (University of Washington)
DTSTART;VALUE=DATE-TIME:20200903T170000Z
DTEND;VALUE=DATE-TIME:20200903T180000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/46
DESCRIPTION:Title: Adv
ances in moduli theory\nby Jarod Alper (University of Washington) as p
art of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nWe will survey
how recent advances in moduli theory allow for a new technique to constru
ct projective moduli spaces of objects with potentially non-finite automor
phism groups such as sheaves\, complexes or Fano varieties. We will prim
arily explore this technique through the lens of the moduli space of vecto
r bundles over a smooth curve where the definitions and concepts are most
readily internalized. Time permitting\, we will discuss applications to B
ridgeland stability and perhaps how this construction technique\, which wo
rks now only in characteristic zero\, can be generalized to positive chara
cteristic.\n
LOCATION:https://researchseminars.org/talk/ZAG/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Höring (Université Côte d'Azur)
DTSTART;VALUE=DATE-TIME:20200908T100000Z
DTEND;VALUE=DATE-TIME:20200908T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/47
DESCRIPTION:Title: Fan
o manifolds such that the tangent bundle is (not) big\nby Andreas Hör
ing (Université Côte d'Azur) as part of ZAG (Zoom Algebraic Geometry) se
minar\n\n\nAbstract\nLet X be a Fano manifold. While the properties of the
anticanonical divisor -KX and its multiples have been studied by many aut
hors\, the positivity of the tangent bundle TX is much more elusive. We gi
ve a complete characterisation of the pseudoeffectivity of TX for del Pezz
o surfaces\, hypersurfaces in the projective space and del Pezzo threefold
s. This is joint work with Jie Liu and Feng Shao.\n
LOCATION:https://researchseminars.org/talk/ZAG/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joaquín Moraga (Princeton University)
DTSTART;VALUE=DATE-TIME:20200910T150000Z
DTEND;VALUE=DATE-TIME:20200910T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/48
DESCRIPTION:Title: Top
ology and geometry of Kawamata log terminal singularities\nby Joaquín
Moraga (Princeton University) as part of ZAG (Zoom Algebraic Geometry) se
minar\n\n\nAbstract\nIn this talk\, we will discuss the topology of Kawama
ta log terminal singularities. We show that from the perspective of the fu
ndamental group klt singularities are close to quotient singularities. For
instance\, the regional fundamental group of a klt singularity of dimensi
on n contains a normal abelian subgroup of rank at most n and index at mos
t c(n). Then\, we proceed to study geometric implications of the topology
of klt singularities. We give a characterization theorem in the case that
the abelian part of the fundamental group is large of full rank.\n
LOCATION:https://researchseminars.org/talk/ZAG/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julie Rana (Lawrence University)
DTSTART;VALUE=DATE-TIME:20200915T150000Z
DTEND;VALUE=DATE-TIME:20200915T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/49
DESCRIPTION:Title: Sin
gularities and divisors in the moduli space of surfaces\nby Julie Rana
(Lawrence University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\
n\nAbstract\nThe KSBA moduli space of stable surfaces (surfaces with slc s
ingularities and ample canonical class) is a natural compactification of G
ieseker's moduli space of surfaces of general type. In contrast with the m
oduli space of curves\, very little is known about the birational geometry
of KSBA moduli spaces\; indeed\, there are very few examples of divisors
in KSBA moduli spaces. I will give an example of a divisor in the moduli s
pace of quintic surfaces corresponding to surfaces with cyclic quotient si
ngularities. I also discuss joint work with Giancarlo Urz\\'ua where we gi
ve bounds that help to narrow the search.\n
LOCATION:https://researchseminars.org/talk/ZAG/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Varilly-Alvarado (Rice University)
DTSTART;VALUE=DATE-TIME:20200527T150000Z
DTEND;VALUE=DATE-TIME:20200527T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/50
DESCRIPTION:Title: Rat
ional curves on K3 surfaces\nby Anthony Varilly-Alvarado (Rice Univers
ity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ZAG/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Louis Colliot-Thelene (Université Paris-Sud)
DTSTART;VALUE=DATE-TIME:20200922T140000Z
DTEND;VALUE=DATE-TIME:20200922T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/51
DESCRIPTION:Title: Zer
o-cycles on del Pezzo surfaces\nby Jean-Louis Colliot-Thelene (Univers
ité Paris-Sud) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbst
ract\nLet k be an arbitary field of characteristic zero and X be a smooth\
, projective\, geometrically rational surface. Birational classification o
f such surfaces (over k) is due to Enriques\, Manin\, Iskovskikh\, Mori. W
e are interested in zero-cycles on such surfaces. In 1974\, Daniel Coray s
howed that on a smooth cubic surface X with a closed point of degree prim
e to 3 there exists a closed point of degree 1\, 4 or 10. Whether 4 and 10
may be omitted is still an open question. We first show how a combination
of generisation\, specialisation\, Bertini theorems and "large" fields a
voids considerations of special cases in Coray's argument. For smooth cubi
c surfaces X with a rational point\, we show that any zero-cycle of degree
at least 10 is rationally equivalent to an effective cycle. We establish
analogues of these results for del Pezzo surfaces X of degree 2 and of deg
ree 1. This completes the proof that for any geometrically rational surfac
e X with a rational point\, there exists an integer N which depends only
on the geometry of the surface\, such that any zero-cycle of degree at le
ast N is rationally equivalent to an effective zero-cycle. For smooth cubi
c surfaces X without a rational point\, we relate the question whether the
re exists a degree 3 point which is not on a line to the question whether
rational points are dense on a del Pezzo surface of degree 1.\n
LOCATION:https://researchseminars.org/talk/ZAG/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Thompson (Loughborough University)
DTSTART;VALUE=DATE-TIME:20200924T150000Z
DTEND;VALUE=DATE-TIME:20200924T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/52
DESCRIPTION:Title: Mir
ror symmetry for fibrations and degenerations\nby Alan Thompson (Lough
borough University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n
Abstract\nIn a 2004 paper\, Tyurin briefly hinted at a novel relationship
between Calabi-Yau mirror symmetry and the Fano-LG correspondence. More sp
ecifically\, if one can degenerate a Calabi-Yau manifold to a pair of (qua
si-)Fanos\, then one expects to be able to express the mirror Calabi-Yau i
n terms of the corresponding Landau-Ginzburg models. Some details of this
correspondence were worked out by C. F. Doran\, A. Harder\, and I in a 201
7 paper\, but much remains mysterious. In this talk I will describe recent
attempts to better understand this picture\, and how it hints at a broade
r mirror symmetric correspondence between degeneration and fibration struc
tures. As an example of this correspondence\, I will discuss the question
of finding mirrors to certain exact sequences which describe the Hodge the
ory of degenerations. The material in this talk is joint work in progress
with C. F. Doran.\n
LOCATION:https://researchseminars.org/talk/ZAG/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Zarhin (Penn State University)
DTSTART;VALUE=DATE-TIME:20200929T140000Z
DTEND;VALUE=DATE-TIME:20200929T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/53
DESCRIPTION:Title: Jor
dan properties of automorphism groups of algebraic varieties and complex m
anifolds\nby Yuri Zarhin (Penn State University) as part of ZAG (Zoom
Algebraic Geometry) seminar\n\n\nAbstract\nA classical theorem of Jordan a
sserts that each finite subgroup of the complex general linear group GL(n)
is "almost commutative": it contains a commutative normal subgroup with
index bounded by an universal constant that depends only on n. We discuss
an analogue of this property for the groups of birational (and biregular)
automorphisms of complex algebraic varieties and the groups of bimeromorp
hic automorphisms of compact complex manifolds.\n
LOCATION:https://researchseminars.org/talk/ZAG/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Burt Totaro (UCLA)
DTSTART;VALUE=DATE-TIME:20201001T160000Z
DTEND;VALUE=DATE-TIME:20201001T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/54
DESCRIPTION:Title: The
Hilbert scheme of points on affine space\nby Burt Totaro (UCLA) as pa
rt of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will discuss
the Hilbert scheme of d points in affine n-space\, with some examples. Thi
s space has many irreducible components for n at least 3 and has been poor
ly understood. For n greater than d\, we determine the homotopy type of th
e Hilbert scheme in a range of dimensions. Many questions remain. (Joint w
ith Marc Hoyois\, Joachim Jelisiejew\, Denis Nardin\, Maria Yakerson.)\n
LOCATION:https://researchseminars.org/talk/ZAG/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junliang Shen (MIT)
DTSTART;VALUE=DATE-TIME:20201006T160000Z
DTEND;VALUE=DATE-TIME:20201006T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/55
DESCRIPTION:Title: Coh
omology of the moduli of Higgs bundles and the Hausel-Thaddeus conjecture<
/a>\nby Junliang Shen (MIT) as part of ZAG (Zoom Algebraic Geometry) semin
ar\n\n\nAbstract\nWe describe the cohomological structure of the moduli sp
ace of stable SL_n Higgs bundles on a curve following the topological mirr
or symmetry conjecture of Hausel-Thaddeus. For the approach\, we establish
a connection between:\n(a) the moduli space of twisted Higgs bundles by a
n effective divisor of degree greater than 2g-2\, and\n(b) the moduli spac
e of K_C-Higgs bundles\,\nusing vanishing cycle functors. This allows us t
o apply Ngo's support theorem\, which has a simpler form in the case (a) (
by Ngo\, Chaudouard-Laumon\, de Cataldo)\, to the case of (b) which concer
ns hyper-Kähler geometries. In particular\, this gives a new proof of the
Hausel-Thaddeus conjecture proven previously by Gröchenig-Wyss-Ziegler v
ia p-adic integrations. Based on joint work with Davesh Maulik.\n
LOCATION:https://researchseminars.org/talk/ZAG/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Logvinenko (Cardiff University)
DTSTART;VALUE=DATE-TIME:20201008T153000Z
DTEND;VALUE=DATE-TIME:20201008T163000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/56
DESCRIPTION:Title: Ske
in-triangulated representations of generalised braids\nby Timothy Logv
inenko (Cardiff University) as part of ZAG (Zoom Algebraic Geometry) semin
ar\n\n\nAbstract\nOrdinary braid group Br_n is a well-known algebraic stru
cture which encodes configurations of n non-touching strands (“braids”
) up to continious transformations (“isotopies”). A classical result o
f Khovanov and Thomas states that there is a natural categorical action of
Br_n on the derived category of the cotangent bundle of the variety of co
mplete flags in C^n.\nIn this talk\, I will introduce a new structure: the
category GBr_n of generalised braids. These are the braids whose strands
are allowed to touch in a certain way. They have multiple endpoint configu
rations and can be non-invertible\, thus forming a category rather than a
group. In the context of triangulated categories\, it is natural to impose
certain relations which result in the notion of a skein-triangulated repr
esentation of GBr_n.\nA decade-old conjecture states that there a skein-tr
iangulated action of GBr_n on the cotangent bundles of the varieties of fu
ll and partial flags in C^n. We prove this conjecture for n = 3. We also s
how that any categorical action of Br_n can be lifted to a skein-triangula
ted action of GBr_n\, which behaves like a categorical nil Hecke algebra.
This is a joint work with Rina Anno and Lorenzo De Biase.\n
LOCATION:https://researchseminars.org/talk/ZAG/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana-Maria Castravet (Université de Versailles St-Quentin-en-Yveli
nes)
DTSTART;VALUE=DATE-TIME:20201013T140000Z
DTEND;VALUE=DATE-TIME:20201013T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/57
DESCRIPTION:Title: Blo
wn-up toric surfaces with non-polyhedral effective cone\nby Ana-Maria
Castravet (Université de Versailles St-Quentin-en-Yvelines) as part of ZA
G (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will report on recent
joint work with Antonio Laface\, Jenia Tevelev and Luca Ugaglia.\nWe cons
truct examples of projective toric surfaces whose blow-up at a general poi
nt has a\nnon-polyhedral pseudoeffective cone\, both in characteristic 0 a
nd in prime characteristic.\nAs a consequence\, we prove that the pseudo-e
ffective cone of the Grothendieck-Knudsen moduli space of stable\, n-point
ed\, rational stable curves\, is not polyhedral if\nn>=10 in characterist
ic 0 and in positive characteristic for an infinite set of primes of posit
ive density.\nIn particular\, these moduli spaces are not Mori dream space
s even in positive characteristic.\n
LOCATION:https://researchseminars.org/talk/ZAG/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandra Di Rocco (KTH)
DTSTART;VALUE=DATE-TIME:20201015T140000Z
DTEND;VALUE=DATE-TIME:20201015T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/58
DESCRIPTION:Title: Alg
ebraic Geometry of Data\nby Sandra Di Rocco (KTH) as part of ZAG (Zoom
Algebraic Geometry) seminar\n\n\nAbstract\nIt is often convenient to visu
alise algebraic varieties (and hence systems of polynomial equations) by
sampling. The key challenge is to have the right distribution and density
in order to recover the shape\, i.e the topology of the variety. Bottlenec
ks are pairs of points on the variety joined by a line which is normal to
the variety at both points. These points play a special role in determinin
g the appropriate density of a point-sample. Under suitable genericity ass
umptions the number of bottlenecks of an affine variety is finite and we c
all it the bottleneck degree. We show that it is determined by (classical)
invariants of the variety\, i.e. polar classes. The talk is based on join
t work with D. Eklund and M. Weinstein.\n
LOCATION:https://researchseminars.org/talk/ZAG/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gergely Berczi (Aarhus University)
DTSTART;VALUE=DATE-TIME:20201020T150000Z
DTEND;VALUE=DATE-TIME:20201020T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/59
DESCRIPTION:Title: Non
-reductive group actions and hyperbolicity\nby Gergely Berczi (Aarhus
University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract
\nNon-reductive reparametrisation group actions play central role in hyper
bolicity questions. Using recently developed intersection theory on non-re
ductive geometric invariant theory-type quotients and following the strate
gy of Demailly\, Siu et al\, last year we completed a proof of the Green-G
riffiths-Lang and Kobayashi hyperbolicity conjectures for generic hypersur
faces of polynomial degree. We explain elements of the proof. Joint work w
ith F. Kirwan.\n
LOCATION:https://researchseminars.org/talk/ZAG/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Mumford (Harvard University and Brown University)
DTSTART;VALUE=DATE-TIME:20200625T160000Z
DTEND;VALUE=DATE-TIME:20200625T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/60
DESCRIPTION:Title: Q&A
with legendary geometers: David Mumford\nby David Mumford (Harvard Un
iversity and Brown University) as part of ZAG (Zoom Algebraic Geometry) se
minar\n\n\nAbstract\nQ&A with David Mumford (please\, no algebraic geometr
y questions). If you want to ask a question you should e-mail it in advanc
e to i.cheltsov@ed.ac.uk\n
LOCATION:https://researchseminars.org/talk/ZAG/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Liedtke (Technical University of Munich)
DTSTART;VALUE=DATE-TIME:20200917T150000Z
DTEND;VALUE=DATE-TIME:20200917T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/61
DESCRIPTION:Title: Rat
ional curves on K3 surfaces\nby Christian Liedtke (Technical Universit
y of Munich) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac
t\nWe prove that every complex projective K3 surface contains infinitely r
ational curves\, which confirms a folklore conjecture on K3 surfaces. This
was previously known for elliptic K3 surfaces (Bogomolov-Tschinkel)\, for
very general K3 surfaces (Chen)\, as well as for K3 surfaces of odd Picar
d rank (Bogomolov-Hassett-Tschinkel\, Li-Liedtke). We finish this conjectu
re by introducing two new techniques: “regeneration” (a sort of conver
se to degeneration) and the “marked point trick” (a technique for cont
rolled degenerations)\, which allows to treat the missing cases. This is j
oint work with Xi Chen and Frank Gounelas.\n
LOCATION:https://researchseminars.org/talk/ZAG/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Borisov (Binghamton University)
DTSTART;VALUE=DATE-TIME:20201022T150000Z
DTEND;VALUE=DATE-TIME:20201022T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/62
DESCRIPTION:Title: Pro
jective geometry approach to Jacobian Conjecture\nby Alexander Borisov
(Binghamton University) as part of ZAG (Zoom Algebraic Geometry) seminar\
n\n\nAbstract\nacobian Conjecture is one of the oldest unsolved problems i
n Algebraic Geometry\, going back to a 1939 paper by Keller. It is infamou
s for the large number of incorrect proofs that have been proposed over th
e years. In fact\, it is quite possible that the conjecture is false\, esp
ecially in higher dimensions. For the past 10-15 years I have been making
slow but steady progress in understanding this enigma in dimension two\, u
sing classical methods of algebraic geometry of projective surfaces and so
me inspiration from the Minimal Model Program. I will explain my approach
and where it has led me\, and will also discuss some related conjectures.\
n
LOCATION:https://researchseminars.org/talk/ZAG/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Greb (University of Duisburg-Essen)
DTSTART;VALUE=DATE-TIME:20201027T160000Z
DTEND;VALUE=DATE-TIME:20201027T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/63
DESCRIPTION:Title: Pro
jective flatness over klt spaces and uniformisation of varieties with nef
anti-canonical divisor\nby Daniel Greb (University of Duisburg-Essen)
as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will dis
cuss a criterion for the projectivisation of a reflexive sheaf on a klt sp
ace to be induced by a projective representation of the fundamental group
of the smooth locus. This criterion is then applied to give a characterisa
tion of finite quotients of projective spaces and Abelian varieties by Q-C
hern class (in)equalities and a suitable stability condition. This stabili
ty condition is formulated in terms of a naturally defined extension of th
e tangent sheaf by the structure sheaf. I will further examine cases in wh
ich this stability condition is satisfied\, comparing it to K-semistabilit
y and related notions. This is joint work with Stefan Kebekus and Thomas P
eternell.\n
LOCATION:https://researchseminars.org/talk/ZAG/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junyan Cao (Université Côte d'Azur)
DTSTART;VALUE=DATE-TIME:20201029T140000Z
DTEND;VALUE=DATE-TIME:20201029T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/64
DESCRIPTION:Title: On
the Ohsawa-Takegoshi extension theorem\nby Junyan Cao (Université Cô
te d'Azur) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\
nAbstract: Since it was established\, the Ohsawa-Takegoshi extension theor
em turned out to be a fundamental tool in complex geometry. We establish a
new extension result for twisted canonical forms defined on a hypersurfac
e with simple normal crossings of a projective manifold with a control on
its L^2 norme. It is a joint work with Mihai Paun.\n
LOCATION:https://researchseminars.org/talk/ZAG/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bianca Viray (University of Washington)
DTSTART;VALUE=DATE-TIME:20201103T170000Z
DTEND;VALUE=DATE-TIME:20201103T180000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/65
DESCRIPTION:Title: On
quadratic points on intersections of two quadrics\nby Bianca Viray (Un
iversity of Washington) as part of ZAG (Zoom Algebraic Geometry) seminar\n
\n\nAbstract\nSpringer's theorem and the Amer-Brumer theorem together impl
y that intersections of two quadrics have a rational point if and only if
they have a 0-cycle of degree 1. In this talk\, we consider whether this
statement can be strengthened in the case when there is no rational point\
, namely when 1) the least degree of a 0-cycle can be 2\, and 2) when this
occurs\, whether there is an effective 0-cycle of degree 2. We report on
results in this direction\, paying particular attention to the case of lo
cal and global fields. This is joint work with Brendan Creutz.\n
LOCATION:https://researchseminars.org/talk/ZAG/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristiano Spotti (Aarhus University)
DTSTART;VALUE=DATE-TIME:20201105T130000Z
DTEND;VALUE=DATE-TIME:20201105T140000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/66
DESCRIPTION:Title: Geo
metric aspects of Kaehler-Einstein metrics on klt pairs\nby Cristiano
Spotti (Aarhus University) as part of ZAG (Zoom Algebraic Geometry) semina
r\n\n\nAbstract\nIn this talk I will discuss about the existence and geome
tric properties (e.g.\, tangent cones asymptotics\, metric degenerations\,
etc...) of conical Kähler-Einstein metrics on klt pairs.\n
LOCATION:https://researchseminars.org/talk/ZAG/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksandr Pukhlikov (University of Liverpool)
DTSTART;VALUE=DATE-TIME:20201110T150000Z
DTEND;VALUE=DATE-TIME:20201110T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/67
DESCRIPTION:Title: Rat
ionally connected rational double covers of primitive Fano varieties\n
by Aleksandr Pukhlikov (University of Liverpool) as part of ZAG (Zoom Alge
braic Geometry) seminar\n\n\nAbstract\nWe show that for a Zariski general
hypersurface $V$ of degree $M+1$ in ${\\mathbb P}^{M+1}$ for $M\\geqslant
5$ there are no Galois rational covers $X\\dashrightarrow V$ with an abeli
an Galois group\, where $X$ is a rationally connected variety. In particul
ar\, there are no rational maps $X\\dashrightarrow V$ of degree 2 with $X$
rationally connected. This fact is true for many other families of primit
ive Fano varieties as well and motivates a conjecture on absolute rigidity
of primitive Fano varieties.\n
LOCATION:https://researchseminars.org/talk/ZAG/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jürgen Hausen (University of Tübingen)
DTSTART;VALUE=DATE-TIME:20201112T160000Z
DTEND;VALUE=DATE-TIME:20201112T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/68
DESCRIPTION:Title: Aut
omorphisms of k*-surfaces\nby Jürgen Hausen (University of Tüb
ingen) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAft
er recalling the necessary background on k*-surfaces\, we give a complete
description of the automorhpism group of a non-toric rational normal proje
ctive k*-surface in terms of isotropy group orders and self intersection n
umbers of suitable invariant curves. We also discuss the basic ingredients
and ideas of the proof.\n
LOCATION:https://researchseminars.org/talk/ZAG/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michela Artebani (Universidad de Concepcion)
DTSTART;VALUE=DATE-TIME:20201117T150000Z
DTEND;VALUE=DATE-TIME:20201117T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/69
DESCRIPTION:Title: Cox
rings of K3 surfaces\nby Michela Artebani (Universidad de Concepcion)
as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nGiven a n
ormal complex projective variety X with finitely generated divisor class g
roup\, its Cox ring R(X) is the Cl(X)-graded algebra whose homogeneous pie
ces are Riemann-Roch spaces of divisors of X. This object is particularly
interesting when it is finitely generated\, since in such case X can be ob
tained as a GIT quotient of an open subset of Spec R(X) by the action of a
quasi-torus [1]. Finding a presentation or even a minimal generating set
for R(X) is in general a difficult problem\, already in the case of surfac
es. In this talk\, after an introduction to the subject\, we will concentr
ate on complex projective K3 surfaces\, which are known to have finitely g
enerated Cox ring exactly when their automorphism group is finite [2]. We
show that the Cox ring can be generated by homogeneous elements whose degr
ees are either classes of (-2)-curves\, sums of at most three elements in
the Hilbert basis of the nef cone\, or classes of divisors of the form 2(E
+E')\, where E\,E' are elliptic curves with E.E'=2. As an application\, we
compute Cox rings of Mori dream K3 surfaces of Picard number 3 and 4. Thi
s is joint work with C. Correa Deisler\, A. Laface and X. Roulleau [3\,4].
\n\nReferences.\n[1] I. Arzhantsev\, U. Derenthal\, J. Hausen\, and A. Laf
ace\, Cox rings\, Cambridge Studies in Advanced Mathematics\, vol. 144\, C
ambridge University Press\, Cambridge\, 2015.\n[2] M. Artebani\, J. Hausen
\, and A. Laface\, On Cox rings of K3 surfaces\, Compos. Math. 146 (2010)\
, no. 4\, 964–998. arXiv:0901.0369\n[3] M. Artebani\, C. Correa Deisler\
, and A. Laface\, Cox rings of K3 surfaces of Picard number three\, J. Alg
ebra 565C (2021)\, 598–626. arXiv:1909.01267\n[4] M. Artebani\, C. Corre
a Deisler\, and X. Roulleau\, Mori dream K3 surfaces of Picard number four
: projective models and Cox rings. arXiv:2011.00475.\n
LOCATION:https://researchseminars.org/talk/ZAG/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yukari Ito (Kavli IPMU)
DTSTART;VALUE=DATE-TIME:20201119T100000Z
DTEND;VALUE=DATE-TIME:20201119T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/70
DESCRIPTION:Title: The
McKay correspondence\nby Yukari Ito (Kavli IPMU) as part of ZAG (Zoom
Algebraic Geometry) seminar\n\n\nAbstract\nThe original McKay corresponde
nce was observed by John McKay as a correspondence between a finite subgro
up G of SL(2\,C) and simple Lie algebra in representation theory and devel
oped as a correspondence between the group G and the minimal resolution of
the quotient singularity C^2/G in algebraic geometry. In this talk\, I wi
ll introduce the McKay correspondence in dimension three and show recent p
rogress and open problems.\n
LOCATION:https://researchseminars.org/talk/ZAG/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kazushi Ueda (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20201124T100000Z
DTEND;VALUE=DATE-TIME:20201124T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/71
DESCRIPTION:Title: Non
commutative del Pezzo surfaces\nby Kazushi Ueda (University of Tokyo)
as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAbstract:
We introduce the notion of noncommutative del Pezzo surfaces\, and show th
at a collection of 12-d general vector bundles of certain ranks and degree
s on an elliptic curve produces a noncommutative del Pezzo surface of degr
ee d. We also define the moduli stack of marked noncommutative del Pezzo s
urfaces\, and show that it contains the configuration space of 9-d points
in general position on the projective plane as a locally closed substack.
This is a joint work in progress with Tarig Abdelgadir and Shinnosuke Okaw
a.\n
LOCATION:https://researchseminars.org/talk/ZAG/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuji Odaka (Kyoto University)
DTSTART;VALUE=DATE-TIME:20201126T100000Z
DTEND;VALUE=DATE-TIME:20201126T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/72
DESCRIPTION:Title: On
compactifying moduli and degenerations of K-trivial varieties\nby Yuji
Odaka (Kyoto University) as part of ZAG (Zoom Algebraic Geometry) seminar
\n\n\nAbstract\nSome background review: the KSBA moduli of varieties of am
ple canonical classes is interpreted via K-stability resp.\, KE metrics (O
’10\, resp.\, Berman-Guenancia’13). A recent trend since 2012 is to es
tablish its Fano analogue\, and study their K-stability itself\, which sti
ll continues to be developed by more and more contributors wonderfully. Lu
ckily\, in both cases\, K-polystable / KE varieties (should) form projecti
ve (compact) moduli schemes.\nHowever\, nevertheless of general K-moduli e
xpectation\, such existence of projective moduli of K-polystable/cscK (pol
arized) varieties is NOT true “at the boundary”\, even for classical K
-trivial / Calabi-Yau cases. Indeed\, as a general theory\, no “canonica
l” algebro-geometric compactification theory of moduli of polarized CY v
ars seems established. E.g. An idea pursued and fairly developed is to att
ach ample extra divisors on the CY vars (to pass to “K:ample”-like sit
uations) and take their “log KSBA” compactifications\, but different c
hoice of the extra divisors can lead to different log KSBA compactificatio
ns.\nIn our talk\, based on our several recent papers (partially j.w.w. Yo
shiki Oshima)\, we discuss the possibilities of still getting “canonical
(geometric) compactifications” of the moduli of polarized K-trivial /
CY varieties and corresponding "canonical limits"\, especially giving mor
e explicit conjectures in hyperKahler / K3 case\, with certain confirmatio
ns. This involves not only classical AG but also DG of collapsing CY metri
cs\, symmetric space theory (Lie\, Cartan\, .. Satake..)\, non-archimedean
/tropical geometry\, and some mirror symmetric phenomena. Examples and pic
tures will be used for the illustration.\n
LOCATION:https://researchseminars.org/talk/ZAG/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takuzo Okada (Saga University)
DTSTART;VALUE=DATE-TIME:20201201T100000Z
DTEND;VALUE=DATE-TIME:20201201T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/73
DESCRIPTION:Title: K-s
tability of birationally superrigid Fano 3-fold weighted hypersurfaces
\nby Takuzo Okada (Saga University) as part of ZAG (Zoom Algebraic Geometr
y) seminar\n\n\nAbstract\nFor Fano varieties\, birational superrigidity an
d K-stability are completely different notions. On the other hand\, they a
re both related to mildness of singularities of (pluri-)anticanonical divi
sors/systems. In fact\, it is conjectured that a birational superrigid Fan
o variety is K-stable. In my talk I will explain recent results that give
a positive answer to the conjecture for Fano 3-fold weighted hypersurfaces
. This is a joint work with In-Kyun Kim and Joonyeong Won.\n
LOCATION:https://researchseminars.org/talk/ZAG/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hulya Arguz (Versailles Saint-Quentin-en-Yvelines University)
DTSTART;VALUE=DATE-TIME:20201203T130000Z
DTEND;VALUE=DATE-TIME:20201203T140000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/74
DESCRIPTION:Title: Enu
merating punctured log Gromov-Witten invariants from wall-crossing\nby
Hulya Arguz (Versailles Saint-Quentin-en-Yvelines University) as part of
ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nPunctured log Gromov
—Witten invariants of Abramovich—Chen--Gross—Siebert are obtained by
counting of stable maps with prescribed tangency conditions (which are al
lowed to be negative) relative to a not necessarily smooth divisor. In thi
s talk we describe an algorithmic method to compute punctured log Gromov-W
itten invariants of log Calabi-Yau varieties\, which are obtained by blowi
ng-up of toric varieties along hypersurfaces on the toric boundary. For th
is we use tropical geometry and wall-crossing computations. This is joint
work with Mark Gross (arxiv:2007.08347).\n
LOCATION:https://researchseminars.org/talk/ZAG/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keiji Oguiso (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20201208T110000Z
DTEND;VALUE=DATE-TIME:20201208T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/75
DESCRIPTION:by Keiji Oguiso (University of Tokyo) as part of ZAG (Zoom Alg
ebraic Geometry) seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ZAG/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artan Sheshmani (Harvard University Center for Mathematical scienc
es and Applications)
DTSTART;VALUE=DATE-TIME:20201210T150000Z
DTEND;VALUE=DATE-TIME:20201210T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/76
DESCRIPTION:Title: DT
invariants from Gerstenhaber-BV structures\, and degeneration technique\nby Artan Sheshmani (Harvard University Center for Mathematical sciences
and Applications) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA
bstract\nWe discuss Donaldson-Thomas (DT) invariants of torsion sheaves wi
th 2 dimensional support on a smooth projective surface in an ambient non-
compact Calabi Yau fourfold given by the total space of a rank 2 bundle on
the surface. We prove that in certain cases\, when the rank 2 bundle is c
hosen appropriately\, the universal truncated Atiyah class of these codime
nsion 2 sheaves reduces to one\, defined over the moduli space of such she
aves realized as torsion codimension 1 sheaves in a noncompact divisor (th
reefold) embedded in the ambient fourfold. Such reduction property of univ
ersal Atiyah class enables us to relate our fourfold DT theory to a reduce
d DT theory of a threefold and subsequently then to the moduli spaces of s
heaves on the base surface. We finally make predictions about modularity o
f such fourfold invariants when the base surface is an elliptic K3. There
are connections between these invariants and birational properties of the
base surface which we will discuss if time permits.\n
LOCATION:https://researchseminars.org/talk/ZAG/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sho Tanimoto (Kumamoto University)
DTSTART;VALUE=DATE-TIME:20201215T110000Z
DTEND;VALUE=DATE-TIME:20201215T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/77
DESCRIPTION:Title: Rat
ional curves on Fano threefolds\nby Sho Tanimoto (Kumamoto University)
as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nMori prov
ed that a smooth Fano variety contains a lots of rational curves using fam
ous Bend and Break technique. Thus it is natural to study the space of rat
ional curves on a smooth Fano variety. Lines and conics on Fano threefolds
are well studied\, and one may ask what one can say about higher degree r
ational curves. Recently we established Movable Bend and Break for Fano th
reefolds claiming that any free curve of high degree breaks into the union
of two free curves. A proof is intricate\, and it relies on many properti
es of three dimensional MMP such as Mori’s classification of divisorial
contractions on smooth projective threefolds. In this talk I would like to
explain some aspects of our proof of Movable Bend and Break as well as an
application to Batyrev’s conjecture predicting a polynomial growth of t
he number of components of bounded degree for the moduli space of rational
curves. If time permits\, then I also explain a relation of our study to
Geometric Manin’s conjecture which is an inspiration of our study. This
is joint work with Roya Beheshti\, Brian Lehmann\, and Eric Riedl.\n
LOCATION:https://researchseminars.org/talk/ZAG/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Harder (Lehigh University)
DTSTART;VALUE=DATE-TIME:20201217T160000Z
DTEND;VALUE=DATE-TIME:20201217T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/78
DESCRIPTION:Title: Log
symplectic pairs and mixed Hodge structures\nby Andrew Harder (Lehigh
University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac
t\nA log symplectic pair is a pair (X\,Y) consisting of a smooth projectiv
e variety X and a divisor Y in X so that there is a non-degenerate log 2-f
orm on X with poles along Y. I will discuss the relationship between log s
ymplectic pairs and degenerations of hyperkaehler varieties\, and how this
naturally leads to a class of log symplectic pairs called log symplectic
pairs of "pure weight". I will talk about common properties of cohomology
rings of log symplectic pairs of pure weight and type III degenerations of
hyperkaehler varieties\, in particular\, the fact that both have the curi
ous hard Lefschetz' (CHL) property discovered by Hausel and Rodriguez-Vill
egas. Finally I will discuss partial results towards proving that in both
of these cases\, the CHL property is a consequence of P=W type results. Pa
rt of this is based on work with Li\, Shen\, and Yin.\n
LOCATION:https://researchseminars.org/talk/ZAG/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Han-Bom Moon (Fordham University)
DTSTART;VALUE=DATE-TIME:20201222T150000Z
DTEND;VALUE=DATE-TIME:20201222T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/79
DESCRIPTION:Title: Poi
nt configurations\, phylogenetic trees\, and dissimilarity vectors\nby
Han-Bom Moon (Fordham University) as part of ZAG (Zoom Algebraic Geometry
) seminar\n\n\nAbstract\nIn 2004 Pachter and Speyer introduced the dissimi
larity maps for phylogenetic trees and asked two important questions about
their relationship with tropical Grassmannian. Multiple authors answered
affirmatively the first of these questions\, showing that dissimilarity ve
ctors lie on the tropical Grassmannian\, but the second question\, whether
the set of dissimilarity vectors forms a tropical subvariety\, remained o
pened. In this talk\, we present a weighted variant of the dissimilarity m
ap and show that weighted dissimilarity vectors form a tropical subvariety
of the tropical Grassmannian in exactly the way that Pachter-Speyer envis
ioned. This tropical variety has a geometric interpretation in terms of po
int configurations on rational normal curves. This is joint work with Ales
sio Caminata\, Noah Giansiracusa\, and Luca Schaffler.\n
LOCATION:https://researchseminars.org/talk/ZAG/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hokuto Uehara (Tokyo Metropolitan University)
DTSTART;VALUE=DATE-TIME:20201224T100000Z
DTEND;VALUE=DATE-TIME:20201224T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/80
DESCRIPTION:Title: Exc
eptional collections on the Hilzebruch surface of degree 2\nby Hokuto
Uehara (Tokyo Metropolitan University) as part of ZAG (Zoom Algebraic Geom
etry) seminar\n\n\nAbstract\nThe purpose of my talk is to clarify the stru
cture of exceptional collections of the derived category of coherent sheav
es on the Hirzebruch surface of degree 2 (a special weak del Pezzo surface
)\, to the extent it is understood by Orlov and Kuleshov for del Pezzo sur
faces.\n (1) First\, we prove that for any exceptional object in it\, one
can find an autoequivalence which sends it to an exceptional vector bundle
.\nThis result was conjectured by Shinnosuke Okawa and the speaker in 2015
.\n (2) Refining the method of the proof of the above result\, and based o
n a deformation argument\, we prove that the braid group on 4 strands acts
transitively (up to shifts) on the set of exceptional collections of leng
th 4. This is a special case of an old conjecture by Bondal and Polishchuk
.\n (3) We also prove that any exceptional collection can be extended to a
full exceptional collection.\nMy talk is based on a joint work with Shinn
osuke Okawa (Osaka) and Akira Ishii (Nagoya).\n
LOCATION:https://researchseminars.org/talk/ZAG/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingjun Han (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20201229T150000Z
DTEND;VALUE=DATE-TIME:20201229T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/81
DESCRIPTION:Title: The
ACC for local volumes and boundedness of singularities\nby Jingjun Ha
n (Johns Hopkins University) as part of ZAG (Zoom Algebraic Geometry) semi
nar\n\n\nAbstract\nKawamata log terminal (klt) singularities form an impor
tant class of singularities due to its fundamental roles in MMP\, K\\”ah
ler-Einstein geometry\, and K-stability. Recently\, Chi Li introduced a ne
w invariant called the local volume of a klt singularity which encodes lot
s of interesting geometric and topological information. A folklore conject
ure predicts that local volumes satisfy the ascending chain condition (ACC
) when the coefficients of the boundary divisors belong to a DCC set. In t
his talk\, we will show the ACC conjecture for local volumes holds when th
e ambient variety is fixed. We will also explore the relation between log
canonical thresholds\, local volumes\, and delta-plt blow-ups. This is bas
ed on ongoing joint work with Yuchen Liu and Lu Qi.\n
LOCATION:https://researchseminars.org/talk/ZAG/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiromichi Takagi (Gakushuin University)
DTSTART;VALUE=DATE-TIME:20210107T100000Z
DTEND;VALUE=DATE-TIME:20210107T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/84
DESCRIPTION:Title: Key
varieties for prime Q-Fano threefolds of codimension 4\nby Hiromichi
Takagi (Gakushuin University) as part of ZAG (Zoom Algebraic Geometry) sem
inar\n\n\nAbstract\nI talk about my construction of key varieties for prim
e Q-Fano threefolds of codimension 4 related with (P^2)^2-fibrations.I dis
cuss their relations with the cluster variety constructed by Coughlan and
Ducat.\n
LOCATION:https://researchseminars.org/talk/ZAG/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patricio Gallardo (UC Riverside)
DTSTART;VALUE=DATE-TIME:20210112T180000Z
DTEND;VALUE=DATE-TIME:20210112T190000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/85
DESCRIPTION:Title: Com
pactifications of the moduli space of cubic surfaces\nby Patricio Gall
ardo (UC Riverside) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n
Abstract\nWe discuss the interplay between geometric and Hodge theoretical
compactifications for the moduli space of cubic surfaces. In particular\,
we prove that Naruki's compactification is toroidal and has a modular int
erpretation in terms of stable pairs. This last is joint work with Matt K
err and Luca Schaffler. If time allows\, we will describe open questions
and ongoing generalizations of such a relationship to the case of pairs in
volving cubic surfaces and their anticanonical divisors.\n
LOCATION:https://researchseminars.org/talk/ZAG/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hiromu Tanaka (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20210114T100000Z
DTEND;VALUE=DATE-TIME:20210114T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/86
DESCRIPTION:Title: On
Mori fibre spaces in positive characteristic\nby Hiromu Tanaka (Univer
sity of Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstr
act\nThe minimal model program conjecture predicts that any algebraic vari
ety is birational to either a minimal model or a Mori fibre space.\nIn thi
s talk\, we first summarise some results on Mori fibre spaces in positive
characteristic.\nWe also discuss some open problems related to this topic.
\n
LOCATION:https://researchseminars.org/talk/ZAG/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shihoko Ishii (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20210119T090000Z
DTEND;VALUE=DATE-TIME:20210119T100000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/87
DESCRIPTION:Title: Uni
form bound of the number of weighted blow-ups to compute the minimal log d
iscrepancy for smooth 3-folds\nby Shihoko Ishii (University of Tokyo)
as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn the tal
k I will show that the minimal log discrepancy of every pair consisting of
a smooth 3-fold and a "general" real ideal is computed by the divisor obt
ained by at most two weighted blow ups.\n\nOur proof suggests the followi
ng conjecture:\n\nEvery pair consisting of a smooth N-fold and a ``general
” real ideal is computed by a divisor obtained by at most N-1 weighted b
low ups.\n\nThis is regarded as a weighted blow up version of Mustata-Naka
mura’s conjecture.\n
LOCATION:https://researchseminars.org/talk/ZAG/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osamu Fujino (Osaka University)
DTSTART;VALUE=DATE-TIME:20210121T100000Z
DTEND;VALUE=DATE-TIME:20210121T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/88
DESCRIPTION:Title: On
extremal contractions of log canonical pairs\nby Osamu Fujino (Osaka U
niversity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\
nThe cone and contraction theorem holds for projective log canonical pairs
. Let us consider an extremal contraction morphism of a log canonical pair
. We prove that every irreducible component of the exceptional locus is un
iruled. This result was first proved by Yujiro Kawamata for kawamata log t
erminal pairs. His proof uses a relative Kawamata--Viehweg vanishing theor
em for projective bimeromorphic morphisms of complex analytic spaces and d
oes not work for log canonical pairs. Our approach is based on the theory
of quasi-log schemes and can be applied to more general settings. We need
a semipositivity theorem coming from the theory of variations of mixed Hod
ge structure. We note that we do not use the minimal model program.\n
LOCATION:https://researchseminars.org/talk/ZAG/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frances Kirwan (University of Oxford)
DTSTART;VALUE=DATE-TIME:20210126T140000Z
DTEND;VALUE=DATE-TIME:20210126T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/89
DESCRIPTION:Title: Mod
uli of unstable objects in algebraic geometry\nby Frances Kirwan (Univ
ersity of Oxford) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb
stract\nThe construction of the moduli spaces of stable curves of fixed ge
nus is one of the classical applications of Mumford's geometric invariant
theory (GIT)\, developed in the 1960s\; many other moduli spaces of 'stabl
e' objects can be constructed using GIT\, as well as in other ways. The ai
m of this talk is to explain how recent methods from a version of GIT for
non-reductive group actions can help us to use suitable 'stability conditi
ons' to stratify moduli stacks into locally closed strata such that not on
ly the open 'stable' strata but also the 'unstable' strata have coarse mod
uli spaces. In the case of moduli stacks of bundles over a nonsingular pro
jective curve\, these stratifications refine the stratification by Harder-
Narasimhan type. The talk is based on joint work with Gergely Berczi\, Vic
ky Hoskins and Joshua Jackson.\n
LOCATION:https://researchseminars.org/talk/ZAG/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabrizio Catanese (University of Bayreuth)
DTSTART;VALUE=DATE-TIME:20210128T140000Z
DTEND;VALUE=DATE-TIME:20210128T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/90
DESCRIPTION:Title: Var
ieties of nodal surfaces\, Coding theory\, and cubic discriminants\nby
Fabrizio Catanese (University of Bayreuth) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\n\nAbstract\nNodal Hypersurfaces Y in projective spa
ce are those whose singularities have nondegenerate Hessian. \nBasic nume
rical invariants are the dimension n and the degree d of the hypersurfac
e Y\, and the number \\nu of singular points. \nIf you fix those integers
(n\, d\,\\nu) these hypersurfaces are parametrized by the so-called Noda
l Severi varieties F(n\, d\, \\nu). \nThe first basic questions concernin
g them are: \n1) for which triples is F(n\, d\, \\nu) nonempty ? \n2) Whe
n is it irreducible ? \n\nAlready intriguing is the situation for surfaces
\, indeed for n=2 the answer to 1) is known for d <= 6\, also the maximal
number of nodes \\mu (d) that a nodal surface in 3-space of degree d can
have is known only for d <= 6.\n\nThe known maximizing nodal surfaces (th
ose with \\mu(d) nodes) are: the Cayley cubic\, the Kummer quartic surface
s\, the Togliatti quintics\, the Barth sextic.\n\nAn important chapter in
Coding theory is the theory of binary linear codes\, vector subspaces of a
vector space (Z/2)^n.\n\nI will recall basic notions and methods of codi
ng theory (e.g. the McWilliams identities) and describe some codes relate
d to quadratic forms. \n\nNodal surfaces are related to coding theory via
the first homology of their smooth part: it is a binary code K\, which wa
s used by Beauville to show that\, for d=5 \, \\mu(d) = 31. Coding theory
was also crucial in order to prove that \\mu(6) < = 65. \n\nOur main resu
lts concern the cases d = 4\,5\,6 (d=2\,3 being elementary). \n\nTHM 1. Fo
r d=4 the components of F(4\, \\nu) and their incidence correspondence ar
e determined by their extended codes K’\, which are all the shortenings
of the first Reed Muller code.\n\nWe extend this result to nodal K3 surfa
ces of all degrees\, this sheds light on the case d=5.\n\nTHM 2. For d=5
the codes K occurring are classified\, up to a possible exception. F(5\
, \\nu) is irreducible for \\nu = 31\, and for \\nu = 29\,30\,31 these sur
faces are discriminants of the projection of a cubic hypersurface in 5-s
pace. \n\nTHM 3. For d=6 and \\nu = 65 the codes K\, K’ are uniquely d
etermined\, and can be described explicitly via the Doro-Hall graph\, att
ached to the group \\SigmaL(2\, 25)\, and the geometry of the Barth sextic
. Every 65 nodal sextic occurs as discriminant of the projection of a cub
ic hypersurface in 6-space with < = 33 nodes.\n\n\nIrreducibility for d
=6\, and 65 nodes\, is related to the geometry of nodal cubic hypersurfac
es in n-space\, and of the linear subspaces contained in them.\n\nWe pose
the question whether\, in the case of even dimension n\, the cubic hypers
urface with maximal number of singularities is\nprojectively equivalent to
the Segre cubic s_1=s_3=0 (which is locally rigid).\n\nFor theorem 2 I b
enefited of the cooperation of Sandro Verra\, for theorem 3 of Yonghwa Ch
o\, Michael Kiermaier\, Sascha Kurz and the Linux Cluster of the Universi
taet Bayreuth\, while Davide Frapporti and Stephen Coughlan cooperated f
or the geometry of nodal cubic hypersurfaces.\n
LOCATION:https://researchseminars.org/talk/ZAG/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Donaldson (Imperial College London and Simons Center for Geo
metry and Physics)
DTSTART;VALUE=DATE-TIME:20210202T150000Z
DTEND;VALUE=DATE-TIME:20210202T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/91
DESCRIPTION:Title: Enu
merative geometry\, Fredholm analysis and moduli spaces of surfaces of gen
eral type\nby Simon Donaldson (Imperial College London and Simons Cent
er for Geometry and Physics) as part of ZAG (Zoom Algebraic Geometry) semi
nar\n\n\nAbstract\nIn the first part of the talk we will review some backg
round in deformation theory\, comparing the points of view from algebraic
geometric and differential geometry/global analysis. We will review in ou
tline some known established examples in which a "virtual fundamental clas
s" of a moduli space can be defined. In the second part of the talk we wil
l explore the possibility that these ideas can be applied to moduli spaces
of surfaces of general type using the KSBA compactification. We will make
some standard observations about these moduli spaces\, whose dimension of
ten differs from the virtual dimension. We will illustrate the discussion
by a calculation in the case of sextic surfaces with a particular finite s
ymmetry group.\n
LOCATION:https://researchseminars.org/talk/ZAG/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shinnosuke Okawa (Osaka University)
DTSTART;VALUE=DATE-TIME:20210204T110000Z
DTEND;VALUE=DATE-TIME:20210204T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/92
DESCRIPTION:Title: Mod
uli space of semiorthogonal decompositions\nby Shinnosuke Okawa (Osaka
University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac
t\nSemiorthogonal decomposition (SOD) of triangulated categories is quite
interesting and of fundamental importance for various reasons. For example
\, SOD of the derived category of coherent sheaves is closely related to t
he geometry of varieties\, such as the minimal model program (MMP) among o
thers. It is therefore desirable to understand the general properties of S
ODs\, partly so as to classify SODs of as many triangulated categories as
possible. The purpose of this talk is to explain certain moduli spaces of
SODs which we introduced. To a smooth projective morphism of excellent sch
emes f: X \\to B\, we associate an algebraic space over B which classifies
the SODs of the derived categories of the fibers of f. We will discuss pr
operties and various aspects of this moduli space including applications\,
comparison to MMP\, and open problems.\n
LOCATION:https://researchseminars.org/talk/ZAG/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrica Floris (Université de Poitiers)
DTSTART;VALUE=DATE-TIME:20210209T110000Z
DTEND;VALUE=DATE-TIME:20210209T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/93
DESCRIPTION:Title: Con
nected algebraic groups acting on Fano fibrations over $\\mathbb P^1$\
nby Enrica Floris (Université de Poitiers) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\n\nAbstract\nLet G be a connected algebraic group and
X a variety endowed with a regular action of G and a Mori fibre space X/P
1 whose fibre is a Fano variety of Picard rank at least 2. In this talk I
will explain why there is a proper horizontal subvariety of X which is inv
ariant under the action of G\, alongside with some applications of this re
sult to the classification of connected algebraic subgroups of the Cremona
group in dimension 4. This is a joint work with Jeremy Blanc.\n
LOCATION:https://researchseminars.org/talk/ZAG/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasso de Fernex (University of Utah)
DTSTART;VALUE=DATE-TIME:20210211T180000Z
DTEND;VALUE=DATE-TIME:20210211T190000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/94
DESCRIPTION:Title: Mot
ivic integration on Berkovic spaces\nby Tomasso de Fernex (University
of Utah) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nT
he purpose of the talk is to offer a new perspective on motivic integratio
n. Working over a field with trivial norm\, I will introduce a motivic mea
sure on the Berkovich analytification of an algebraic variety and define i
ntegration in this setting. The construction is geometric with a similar s
pirit as Kontsevich’s original definition\, and leads to the formulation
of a functorial theory which mirrors\, in this aspect\, the functoriality
of Cluckers and Loeser's approach via constructible motivic functions. Th
e approach does not rely on model theory but rather on geometric propertie
s such as resolution of singularities and the weak factorization theorem.
The talk is based on joint work with Chung Ching Lau.\n
LOCATION:https://researchseminars.org/talk/ZAG/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusuke Nakamura (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20210216T110000Z
DTEND;VALUE=DATE-TIME:20210216T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/95
DESCRIPTION:Title: Inv
ersion of adjunction for quotient singularities\nby Yusuke Nakamura (U
niversity of Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n
Abstract\nThe minimal log discrepancy is an invariant of singularities def
ined in birational geometry\, and it is related to the conjecture of termi
nation of flips. In this talk\, we will discuss the minimal log discrepanc
ies of quotient singularities. I will show that the PIA (precise inversion
of adjunction) conjecture holds for quotient singularities. The main tool
of this talk involves the theory of the arc space of a quotient singulari
ty established by Denef and Loeser. This is joint work with Kohsuke Shibat
a.\n
LOCATION:https://researchseminars.org/talk/ZAG/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frediani Paola (Università di Pavia)
DTSTART;VALUE=DATE-TIME:20210218T140000Z
DTEND;VALUE=DATE-TIME:20210218T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/96
DESCRIPTION:Title: A c
anonical Hodge theoretic projective structure on compact Riemann surfaces<
/a>\nby Frediani Paola (Università di Pavia) as part of ZAG (Zoom Algebra
ic Geometry) seminar\n\n\nAbstract\nIn this talk we will show the existenc
e of a canonical projective structure on every compact Riemann surface\, c
oming from Hodge theory. We will show that it differs from the canonical p
rojective structure produced by the uniformisation theorem. In fact the (0
\,1)- component of the differential of the corresponding sections of the m
oduli space of projective structures over the moduli space of curves are d
ifferent. The one corresponding to the projective structure coming from un
iformisation was computed by Zograf and Takhtadzhyan as the Weil-Petersson
Kaehler form on the moduli space of curves. Ours is the pullback via the
Torelli map of a nonzero constant scalar multiple of the Siegel form on t
he moduli space of principally polarised abelian varieties. These are resu
lts obtained in collaboration with I. Biswas\, E. Colombo and G.P. Pirola.
\n
LOCATION:https://researchseminars.org/talk/ZAG/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shing-Tung Yau (Harvard University)
DTSTART;VALUE=DATE-TIME:20210223T153000Z
DTEND;VALUE=DATE-TIME:20210223T163000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/97
DESCRIPTION:Title: Geo
metry of Conifold Transitions\nby Shing-Tung Yau (Harvard University)
as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nConifold t
ransitions were introduced by Clemens\, Reid and Friedman to connect Calab
i-Yau threefolds with different topologies. However\, this operation may p
roduce a complex manifold with trivial canonical bundle which is non-Kahle
r. I will discuss this transition from the point of view of metrics and di
fferential geometry\, and propose a non-Kahler analog of Calabi-Yau metric
s which originates in heterotic string theory. This talk will contain join
t works with T.C. Collins\, J.-X. Fu\, J. Li\, and S. Picard.\n
LOCATION:https://researchseminars.org/talk/ZAG/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Atsushi Ito (Nagoya University)
DTSTART;VALUE=DATE-TIME:20210225T100000Z
DTEND;VALUE=DATE-TIME:20210225T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/98
DESCRIPTION:Title: Lin
ear systems on abelian varieties via M-regularity of Q-twisted sheaves
\nby Atsushi Ito (Nagoya University) as part of ZAG (Zoom Algebraic Geomet
ry) seminar\n\n\nAbstract\nFor an ample line bundle $L$ on an abelian vari
ety $X$\, it is known that $L^n$ is basepoint free if $n \\geq 2$\, projec
tively normal if $n \\geq 3$\, and the ideal of $X$ embedded by $|L^n|$ is
generated by quadrics if $n \\geq 4$. As a generalization of these result
s\, Lazarsfeld conjectures that $L^n$ satisfies property $(N_p)$ if $n \\g
eq p+3$.\nThis conjecture is affirmatively proved by Pareschi and strength
en by Pareschi-Popa by the theory of M-regularity. Recently\, Jiang and Pa
reschi consider (variants of) M-regularity of $\\mathbb{Q}$-twisted sheave
s and it turns out that this is very useful when we study the linear syste
m $|L|$ of $L$ itself\, not only $L^n$ for $n \\geq 2$. In this talk\, I w
ill explain this topic and some recent results.\n
LOCATION:https://researchseminars.org/talk/ZAG/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Cukierman (University of Buenos Aires)
DTSTART;VALUE=DATE-TIME:20210302T150000Z
DTEND;VALUE=DATE-TIME:20210302T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/99
DESCRIPTION:Title: Def
ormations of exterior differential ideals and applications\nby Fernand
o Cukierman (University of Buenos Aires) as part of ZAG (Zoom Algebraic Ge
ometry) seminar\n\n\nAbstract\nThe main theme of this talk is the geometry
of moduli spaces of algebraic singular foliations on smooth projective al
gebraic varieties over the complex numbers. A motivating problem is the de
termination of the irreducible components of such moduli spaces. We plan t
o discuss some basic facts on deformations of exterior differential ideals
. With these tools we study deformations of several types of Pfaff ideals\
, obtaining some new irreducible components of spaces of singular foliatio
ns of any codimension. This is based on joint work with Cesar Massri.\n
LOCATION:https://researchseminars.org/talk/ZAG/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiwamu Watanabe (Chuo University)
DTSTART;VALUE=DATE-TIME:20210304T100000Z
DTEND;VALUE=DATE-TIME:20210304T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/100
DESCRIPTION:Title: Po
sitivity of the exterior power of the tangent bundles\nby Kiwamu Watan
abe (Chuo University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n
\nAbstract\nBy Mori's solution of the Hartshorne conjecture\, the only smo
oth projective variety with ample tangent bundle is the projective space.
As a generalization of the Hartshorne conjecture\, Demially\, Peternell an
d Schneider studied smooth projective varieties with nef tangent bundle. T
hey proved that such variety X admits an étale cover Y such that the Alba
nese map Y \\to Alb(Y) is a smooth morphism whose fibers are smooth Fano v
arieties with nef tangent bundle. In this talk\, we will study smooth proj
ective varieties such that the r-th exterior power of the tangent bundle i
s nef\, paying special attention to the case r=2. This talk is based on th
e paper arXiv:2011.01427.\n
LOCATION:https://researchseminars.org/talk/ZAG/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shunsuke Takagi (University of Tokyo)
DTSTART;VALUE=DATE-TIME:20210309T110000Z
DTEND;VALUE=DATE-TIME:20210309T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/101
DESCRIPTION:Title: De
formations of F-pure and F-regular singularities\nby Shunsuke Takagi (
University of Tokyo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\
nAbstract\nF-regular and F-pure singularities are singularities in positiv
e characteristic defined in terms of Frobenius splitting properties. Ma an
d Schwede recently proved that a normal Q-Gorenstein complex variety has l
og terminal singularities if its reduction modulo p has F-regular singular
ities for a single prime p. I will discuss the analog of their result for
log canonical singularities. I will also explain how F-regular singulariti
es behave under equal and mixed characteristic deformations. This talk is
based on joint work with Kenta Sato.\n
LOCATION:https://researchseminars.org/talk/ZAG/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolina Araujo (IMPA)
DTSTART;VALUE=DATE-TIME:20210311T150000Z
DTEND;VALUE=DATE-TIME:20210311T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/102
DESCRIPTION:Title: Bi
rational geometry of Calabi-Yau pairs and 3-dimensional Cremona transforma
tions\nby Carolina Araujo (IMPA) as part of ZAG (Zoom Algebraic Geomet
ry) seminar\n\n\nAbstract\nAbstract: Recently\, Oguiso addressed the follo
wing question\, attributed to Gizatullin: ``Which automorphisms of a smoot
h quartic K3 surface $D\\subset \\mathbb{P}^3$ are induced by Cremona tran
sformations of the ambient space $\\mathbb{P}^3$?'' When $D\\subset \\math
bb{P}^3$ is a quartic surface\, $(\\mathbb{P}^3\,D)$ is an example of a \
\emph{Calabi-Yau pair}\, that is\, a pair $(X\,D)$ consisting of a normal
projective variety $X$ and an effective Weil divisor $D$ on $X$ such that
$K_X+D\\sim 0$. In this talk\, I will explain a general framework to study
the birational geometry of mildly singular Calabi-Yau pairs. Then I will
focus on the case of singular quartic surfaces $D\\subset \\mathbb{P}^3$.
Our results illustrate how the appearance of increasingly worse singularit
ies in $D$ enriches the birational geometry of the pair $(\\mathbb{P}^3\,
D)$\, and lead to interesting subgroups of the Cremona group of $\\mathbb{
P}^3$. This is a joint work with Alessio Corti and Alex Massarenti.\n
LOCATION:https://researchseminars.org/talk/ZAG/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taro Sano (Kobe University)
DTSTART;VALUE=DATE-TIME:20210316T100000Z
DTEND;VALUE=DATE-TIME:20210316T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/103
DESCRIPTION:Title: Bi
rational boundedness of some Calabi-Yau hypersurfaces\nby Taro Sano (K
obe University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbst
ract\nIt is well-known that complex projective K3 surfaces are connected b
y analytic deformations\, but they are algebraically unbounded. Neverthele
ss\, Reid\, Iano-Fletcher and Kollar-Johnson showed the finiteness of weig
hted Calabi-Yau hypersurfaces. Motivated by this\, we study plt Calabi-Yau
pairs (X\,D) and show finiteness of D in some cases. In particular\, we s
how that anticanonical K3 surfaces form a birationally bounded family. We
also exhibit examples of K3 surfaces of a fixed degree whose birational co
ntractions form an unbounded family\, thus the birational boundedness is o
ptimal in a sense.\n
LOCATION:https://researchseminars.org/talk/ZAG/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Lazda (University of Warwick)
DTSTART;VALUE=DATE-TIME:20210318T150000Z
DTEND;VALUE=DATE-TIME:20210318T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/104
DESCRIPTION:Title: A
Neron-Ogg-Shafarevich criterion for K3 surfaces\nby Chris Lazda (Unive
rsity of Warwick) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb
stract\nThe naive analogue of the Néron-Ogg-Shafarevich criterion fails f
or K3 surfaces\, that is\, there exist K3 surfaces over Henselian\, discre
tely valued fields K\, with unramified etale cohomology groups\, but which
do not admit good reduction over K. Assuming potential semi-stable reduct
ion\, I will show how to correct this by proving that a K3 surface has goo
d reduction if and only if is second cohomology is unramified\, and the as
sociated Galois representation over the residue field coincides with the s
econd cohomology of a certain “canonical reduction” of X. This is join
t work with B. Chiarellotto and C. Liedtke.\n
LOCATION:https://researchseminars.org/talk/ZAG/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Lesieutre (Pennsylvania State University)
DTSTART;VALUE=DATE-TIME:20210323T100000Z
DTEND;VALUE=DATE-TIME:20210323T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/105
DESCRIPTION:Title: Ra
tional surface automorphisms without periodic curves\nby John Lesieutr
e (Pennsylvania State University) as part of ZAG (Zoom Algebraic Geometry)
seminar\n\n\nAbstract\nAlthough there are many examples known of infinite
-order automorphisms of rational surfaces\, in most cases these automorphi
sms have at least one periodic curve C (a curve for which f^n(C) = C for s
ome n). I will explain the construction of a class of rational surfaces w
hich admit a large group of automorphisms with no invariant curves. The e
xample makes use of several classical constructions\, and the surfaces adm
it contructions down to three different Coble surfaces.\n
LOCATION:https://researchseminars.org/talk/ZAG/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Sacca (Columbia University)
DTSTART;VALUE=DATE-TIME:20210325T150000Z
DTEND;VALUE=DATE-TIME:20210325T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/106
DESCRIPTION:Title: Fa
no manifolds associated to hyperkahler manifolds\nby Giulia Sacca (Col
umbia University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb
stract\nIt is known that to some Fano manifolds whose cohomology looks lik
e that of a K3 surface\, one can associate\, via geometric constructions\,
examples of hyperkahler manifolds. In this talk I will report on the firs
t steps of a program whose aim is to reverse this construction: starting f
rom a hyperkahler manifold how to recover geometrically a Fano manifold? T
his is joint work with L. Flapan\, E. Macri\, and K. O'Grady.\n
LOCATION:https://researchseminars.org/talk/ZAG/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katsuhisa Furukawa (Josai University)
DTSTART;VALUE=DATE-TIME:20210330T100000Z
DTEND;VALUE=DATE-TIME:20210330T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/107
DESCRIPTION:Title: On
the singular loci of higher secant varieties of Veronese embeddings\n
by Katsuhisa Furukawa (Josai University) as part of ZAG (Zoom Algebraic Ge
ometry) seminar\n\n\nAbstract\nFor a projective variety X in P^N\, the k-s
ecant variety \\sigma_k(X) is defined to be the closure of the union of k-
planes in P^N spanned by k-points of X. It is well known that \\sigma_{k-1
}(X) is contained in the singular locus of \\sigma_k(X). Let us consider t
he case when X is the image of the Veronese embedding P^n to P^N of degree
d\, where N = \\binom{d+N}{d}-1. In the case of k=3\, K. Han showed that
\\Sing(\\sigma_3(X)) = \\sigma_2(X)\, except when d=4 and n > 2. In the ex
ceptional case\, \\Sing(\\sigma_3(X)) is the union of \\sigma_2(X) and D\,
where D is an irreducible subset. In this talk\, we first give a geometri
c description of this D for k = 3\, and next study the case of k > 3. In p
articular\, I will explain projective techniques with respect to an explic
it calculation of the Gauss map of X and the projection from the incidence
correspondence of \\sigma_k(X). This is a joint work with Kangjin Han.\n
LOCATION:https://researchseminars.org/talk/ZAG/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vyacheslav Shokurov (Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20210401T150000Z
DTEND;VALUE=DATE-TIME:20210401T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/108
DESCRIPTION:Title: Ar
ound a-n-complements\nby Vyacheslav Shokurov (Johns Hopkins University
) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nA genera
l conjecture about a-n-complements will be discussed in connection with st
rict $\\delta$-lc singularities\, generalized pairs and McKernan conjectur
e.\n
LOCATION:https://researchseminars.org/talk/ZAG/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Takehiko Yasuda (Osaka University)
DTSTART;VALUE=DATE-TIME:20210406T100000Z
DTEND;VALUE=DATE-TIME:20210406T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/109
DESCRIPTION:Title: St
ringy motives and local fundamental groups of klt surface singularities in
arbitrary characteristic\nby Takehiko Yasuda (Osaka University) as pa
rt of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn this talk\,
I will speak about an application of stringy motives to local fundamental
groups of klt surface singularities. Xu proved that klt singularities in c
haracteristic zero have finite local fundametal groups. I will explain how
to prove that the same is true in arbitrary characteristic and in dimensi
on two\, which had been unknown in characteristics two and three. The key
of the proof is to study the behavior of stringy motives under quasi-etale
Galois covers of klt singularities. This is a joint work with Javier Carv
ajal-Rojas.\n
LOCATION:https://researchseminars.org/talk/ZAG/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Langer (Institute of Mathematics\, University of Warsaw\, P
oland)
DTSTART;VALUE=DATE-TIME:20210408T130000Z
DTEND;VALUE=DATE-TIME:20210408T140000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/110
DESCRIPTION:Title: Ch
ern classes of vector bundles\nby Adrian Langer (Institute of Mathemat
ics\, University of Warsaw\, Poland) as part of ZAG (Zoom Algebraic Geomet
ry) seminar\n\n\nAbstract\nI will talk about various restrictions on Chern
classes of vector bundles on algebraic varieties. One of the most import
ant is Bogomolov's inequality saying that the degree of the discriminant
of a semistable vector bundle on a smooth complex algebraic variety is non
-negative. The degree zero case essentially corresponds to flat vector bu
ndles. There are also versions of this inequality for Higgs bundles and i
n positive characteristic. I will talk about some applications of Bogomolo
v's inequality and its possible variants in the Chow ring of the variety.\
n
LOCATION:https://researchseminars.org/talk/ZAG/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karl Schwede (University of Utah)
DTSTART;VALUE=DATE-TIME:20210413T170000Z
DTEND;VALUE=DATE-TIME:20210413T180000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/111
DESCRIPTION:Title: Re
cent progress in mixed characteristic higher dimensional algebraic geometr
y\nby Karl Schwede (University of Utah) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\n\nAbstract\nIn characteristic zero birational algebr
aic geometry\, Kawamata-Viehweg vanishing is a centrally important tool.
For some applications in characteristic p > 0\, one may use Frobenius and
perturbations as a replacement for resolution of singularities and Kawamat
a-Viehweg vanishing. This talk will show how to use Bhatt's vanishing the
orem for absolute integral closures mixed characteristic as a replacement
for resolutions and Kawamata-Viehweg vanishing theorems in a number of app
lications. This is joint work with B. Bhatt\, L. Ma\, Z. Patakfalvi\, K.
Tucker\, J. Waldron and J. Witaszek.\n
LOCATION:https://researchseminars.org/talk/ZAG/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yasunari Nagai (Waseda University)
DTSTART;VALUE=DATE-TIME:20210415T100000Z
DTEND;VALUE=DATE-TIME:20210415T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/112
DESCRIPTION:Title: Ra
tional normal quintic curves on a cubic fourfold\nby Yasunari Nagai (W
aseda University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAb
stract\nWe study the moduli of rational normal quintic curves on a cubic f
ourfold and its compactifications with a view toward projective symplectic
geometry. This is a work in progress with Manfred Lehn and Duco van Strat
en.\n
LOCATION:https://researchseminars.org/talk/ZAG/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakub Witaszek (University of Michigan)
DTSTART;VALUE=DATE-TIME:20210420T170000Z
DTEND;VALUE=DATE-TIME:20210420T180000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/113
DESCRIPTION:Title: Re
lative semiampleness in mixed characteristic.\nby Jakub Witaszek (Univ
ersity of Michigan) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\n
Abstract\nIn this talk we will discuss the existence of contractions and b
ase point freeness of line bundles in mixed characteristic in the context
of the arithmetic Minimal Model Program.\n
LOCATION:https://researchseminars.org/talk/ZAG/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandor Kovacs (University of Washington)
DTSTART;VALUE=DATE-TIME:20210422T170000Z
DTEND;VALUE=DATE-TIME:20210422T180000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/114
DESCRIPTION:Title: Ho
dge sheaves for singular families\nby Sandor Kovacs (University of Was
hington) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nT
his is a report on joint work with Behrouz Taji. Given a flat projective m
orphism [f:X\\to B] of complex varieties\, assuming that [B] is smooth\,
we construct a system of reflexive Hodge sheaves on [B] . If in addition
[X] is also smooth then this system gives an extension of the Hodge bundl
e underlying the VHS of the smooth locus of [f] . This in turn provides a
criterion that all VHSs of geometric origin must satisfy. As an independen
t application we prove a singular version of Viehweg's conjecture about ba
se spaces of families of maximal variation.\n
LOCATION:https://researchseminars.org/talk/ZAG/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Tschinkel (Courant Institute of Mathematical Sciences\, New Y
ork University)
DTSTART;VALUE=DATE-TIME:20210427T150000Z
DTEND;VALUE=DATE-TIME:20210427T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/115
DESCRIPTION:Title: Eq
uivariant birational types\nby Yuri Tschinkel (Courant Institute of Ma
thematical Sciences\, New York University) as part of ZAG (Zoom Algebraic
Geometry) seminar\n\n\nAbstract\nI will discuss joint work with A. Kresch
and B. Hassett concerning new invariants in equivariant birational geometr
y and their applications.\n
LOCATION:https://researchseminars.org/talk/ZAG/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Margarida Melo (University of Roma Tre)
DTSTART;VALUE=DATE-TIME:20210429T120000Z
DTEND;VALUE=DATE-TIME:20210429T130000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/116
DESCRIPTION:Title: On
the top weight cohomology of the moduli space of abelian varieties\nb
y Margarida Melo (University of Roma Tre) as part of ZAG (Zoom Algebraic G
eometry) seminar\n\n\nAbstract\nThe moduli space of abelian varieties Ag a
dmits well behaved toroidal compactifications whose dual complex can be gi
ven a tropical interpretation. Therefore\, one can use the techniques rece
ntly developed by Chan-Galatius-Payne in order to understand part of the t
opology of Ag via tropical geometry. In this talk\, which is based in join
t work with Madeleine Brandt\, Juliette Bruce\, Melody Chan\, Gwyneth More
land and Corey Wolfe\, I will explain how to use this setup\, and in parti
cular computations in the perfect cone compactification of Ag\, in order t
o describe its top weight cohomology for g up to 7.\n
LOCATION:https://researchseminars.org/talk/ZAG/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Pe Pereira (Universidad Complutense de Madrid)
DTSTART;VALUE=DATE-TIME:20210504T140000Z
DTEND;VALUE=DATE-TIME:20210504T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/117
DESCRIPTION:Title: Mo
derately Discontinuous Algebraic Topology\nby Maria Pe Pereira (Univer
sidad Complutense de Madrid) as part of ZAG (Zoom Algebraic Geometry) semi
nar\n\n\nAbstract\nAn algebraic or complex analytic subset in C^n has 2 na
tural metrics: the outer metric (restriction of the euclidean metric) and
the inner metric (natural extension of the riemannian metric on the smooth
part). These metrics considered up to bilipschitz mappings are analytic i
nvariants\, that is\, they do not depend on the complex analytic embedding
.\nRecently there is an intense activity in bilipschitz geometry of germs
and degenerations\, enriching and providing finer information on\nproblems
that were studied previously from the topological viewpoint (for multipli
city invariance of the germ or certain equisingularity notions).\nIn the w
orks [1] and [2] we develop a new metric algebraic topology\, called the M
oderately Discontinuous Homology and Homotopy\, in the context of subanaly
tic germs in R^n (with a supplementary metric structure) and more generall
y of (degenerating) subanalytic families. This theory captures bilipschitz
information\, or in other words\, quasi isometric invariants\, and aims t
o codify\, in an algebraic way\, part of the bilipschitz geometry.\nA suba
nalytic germ is topologically a cone over its link and the moderately disc
ontinuous theory captures the different speeds\, with respect to the dista
nce to the origin\, in which the topology of the link collapses towards th
e origin. Similarly\, in a degenerating subanalytic family\, it captures t
he different speeds of collapsing with respect to the family parameter.\nT
he MD algebraic topology satisfies all the analogues of the usual theorems
in Algebraic Topology: long exact sequences for the relative case\, Mayer
Vietoris and Seifert van Kampen for special coverings...\nIn this talk\,
I will present the most important concepts in the theory and some results
or applications that we got until the present.\n[1] (with J. Fernandez de
Bobadilla\, S. Heinze\, E. Sampaio) Moderately discontinuous homology. To
appear in Comm. Pure App. Math.. Available in arXiv: 1910.12552\n[2]
(with J. Fernández de Bobadilla\, S. Heinze) Moderately discontinuous hom
otopy. Submitted. Available in ArXiv:2007.01538\n
LOCATION:https://researchseminars.org/talk/ZAG/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mara Ungureanu (University of Freiburg)
DTSTART;VALUE=DATE-TIME:20210506T140000Z
DTEND;VALUE=DATE-TIME:20210506T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/118
DESCRIPTION:Title: Co
unts of secant planes to varieties\, Virasoro algebras\, and universal pol
ynomials\nby Mara Ungureanu (University of Freiburg) as part of ZAG (Z
oom Algebraic Geometry) seminar\n\n\nAbstract\nFor a curve in projective s
pace\, the varieties parametrising its secant planes are among the most st
udied objects in classical enumerative geometry. We shall start with an i
ntroduction to secant varieties and explain the role of degeneration argum
ents in understanding their geometry. We shall then explore the connectio
n between the enumerative geometry of secant varieties and Virasoro algebr
as on one side\, and tautological integrals on the other.\n
LOCATION:https://researchseminars.org/talk/ZAG/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Kebekus (University of Freiburg)
DTSTART;VALUE=DATE-TIME:20210511T130000Z
DTEND;VALUE=DATE-TIME:20210511T140000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/119
DESCRIPTION:Title: Br
auer-Manin obstruction on a simply connected fourfold and a Mordell theore
m in the orbifold setting\nby Stefan Kebekus (University of Freiburg)
as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAlmost one
decade ago\, Poonen constructed the first examples of algebraic varieties
over global fields for which Skorobogatov's etale Brauer-Manin obstructio
n does not explain the failure of the Hasse principle. By now\, several co
nstructions are known\, but they all share common geometric features such
as large fundamental groups. In this paper\, we construct simply connected
fourfolds over global fields of positive characteristic for which the Bra
uer-Manin machinery fails. Contrary to earlier work in this direction\, ou
r construction does not rely on major conjectures. Instead\, we establish
a new diophantine result of independent interest: a Mordell-type theorem f
or Campana's "geometric orbifolds" over function fields of positive charac
teristic. Along the way\, we also construct the first example of simply co
nnected surface of general type over a global field with a non-empty\, but
non-Zariski dense set of rational points. This is joint work with Jorge P
ereira (IMPA) and Arne Smeets (Nijmegen)\n
LOCATION:https://researchseminars.org/talk/ZAG/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jack Rogers (University of Manchester)
DTSTART;VALUE=DATE-TIME:20210513T140000Z
DTEND;VALUE=DATE-TIME:20210513T150000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/120
DESCRIPTION:Title: K-
stability of smooth Fano SL2-threefolds\nby Jack Rogers (University of
Manchester) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac
t\nThere has been much interest in K-stability since it was shown to be eq
uivalent to the existence of Kähler-Einstein metrics by Chen-Donaldson-Su
n. The theory of K-stability is now well developed\, but practical methods
to check whether a given variety is K-stable are hard to come by. Equivar
iant K-stability\, introduced by Datar-Székelyhidi\, makes finding such c
riteria easier for varieties with large automorphism groups.\n\nIf an alge
braic group G acts on a variety X\, the complexity of the action is the mi
nimal codimension in X of the orbits of a Borel subgroup B of G (e.g. if T
is a torus\, the complexity zero T-varieties are the toric varieties). Co
nditions for K-stability have been found for toric varieties by Wang-Zhu\,
for complexity one T-varieties by Ilten-Süss and for all complexity zero
varieties by Delcroix.\n\nWe will discuss the combinatorial description d
ue to Timashev of complexity one G-varieties\, and describe a practical me
thod to check K-stability in the particular case of smooth Fano SL2-threef
olds. In particular\, this method proves the K-stability of several variet
ies not previously known to be K-stable\, e.g. projective 3-space blown up
along three disjoint lines. This is joint work with Hendrik Süss.\n
LOCATION:https://researchseminars.org/talk/ZAG/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jørgen Vold Rennemo (University of Oslo)
DTSTART;VALUE=DATE-TIME:20210518T110000Z
DTEND;VALUE=DATE-TIME:20210518T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/121
DESCRIPTION:Title: K-
theoretic sheaf counting invariants on C^4\nby Jørgen Vold Rennemo (U
niversity of Oslo) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nA
bstract\nOh and Thomas have recently defined a K-theoretic sheaf counting
invariant for moduli spaces of sheaves on a Calabi-Yau 4-fold. One of the
simplest examples of such a moduli scheme is the Hilbert scheme of n point
s on C^4. The topic of this talk is a proof of a formula for the generatin
g functions of invariants of these Hilbert schemes\, confirming a conjectu
re of Nekrasov (as well a generalisation to Quot schemes of C^4\, conjectu
red by Nekrasov and Piazzalunga). This is joint work with Martijn Kool.\n
LOCATION:https://researchseminars.org/talk/ZAG/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marta Pieropan (Utrecht University)
DTSTART;VALUE=DATE-TIME:20210520T150000Z
DTEND;VALUE=DATE-TIME:20210520T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/122
DESCRIPTION:Title: Ca
mpana points on Fano varieties\nby Marta Pieropan (Utrecht University)
as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nWe call C
ampana points an arithmetic notion of points on Campana's orbifolds that h
as been first studied by Campana and Abramovich\, and that interpolates be
tween the notions of rational and integral points. In this talk we introdu
ce Campana points and a Manin type conjecture for Campana points on Fano v
arieties\, and we present results for equivariant compactifications of vec
tor groups (joint work with A. Smeets\, S. Tanimoto\, T. Várilly-Alvarado
) and for toric varieties (joint work with D. Schindler).\n
LOCATION:https://researchseminars.org/talk/ZAG/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Hassett (Brown University)
DTSTART;VALUE=DATE-TIME:20210525T150000Z
DTEND;VALUE=DATE-TIME:20210525T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/123
DESCRIPTION:Title: Ra
tionality of even-dimensional intersections of two real quadrics\nby B
rendan Hassett (Brown University) as part of ZAG (Zoom Algebraic Geometry)
seminar\n\n\nAbstract\nWe consider rationality constructions for smooth c
omplete intersections of two quadrics over nonclosed fields. Over the real
numbers\, we establish a criterion for rationality in dimension four and
discuss open cases in higher dimensions. (joint with János Kollár and Yu
ri Tschinkel)\n
LOCATION:https://researchseminars.org/talk/ZAG/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Varilly-Alvarado (Rice University)
DTSTART;VALUE=DATE-TIME:20210527T150000Z
DTEND;VALUE=DATE-TIME:20210527T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/124
DESCRIPTION:Title: Qu
asi-hyperbolicity via explicit symmetric differentials\nby Anthony Var
illy-Alvarado (Rice University) as part of ZAG (Zoom Algebraic Geometry) s
eminar\n\n\nAbstract\nA surface X is algebraically quasi-hyperbolic if it
contains finitely many curves of genus 0 or 1. In 2006\, Bogomolov and de
Oliveira used asymptotic computations to show that sufficiently nodal sur
faces of high degree in projective three-space carry symmetric differentia
ls\, and they used this to prove quasi-hyperbolicity of these surfaces. W
e explain how a granular analysis of their ideas\, combined with computati
onal tools and insights\, yield explicit results for the existence of symm
etric differentials\, and we show how these results can be used to give co
nstraints on the locus of rational curves on surfaces like the Barth Decic
\, Buechi's surface\, and certain complete intersections of general type\,
including the surface parametrizing perfect cuboids\, and the surface par
ametrizing magic squares of squares. This is joint work with Nils Bruin a
nd Jordan Thomas.\n
LOCATION:https://researchseminars.org/talk/ZAG/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Livia Campo (University of Birmingham)
DTSTART;VALUE=DATE-TIME:20210601T110000Z
DTEND;VALUE=DATE-TIME:20210601T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/125
DESCRIPTION:Title: Fa
no 3-folds and double covers\nby Livia Campo (University of Birmingham
) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will p
ropose a method to explicitly construct 52 deformation families of termina
l Q-Fano 3-folds in codimension 4 and Fano index 2. Their structure descen
ds from suitably crafted double covers. If time allows\, I will briefly di
scuss the non-solidity of some of such families (in a joint work in progre
ss with T. Guerreiro).\n
LOCATION:https://researchseminars.org/talk/ZAG/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrico Fatighenti (Sapienza - Università di Roma)
DTSTART;VALUE=DATE-TIME:20210603T160000Z
DTEND;VALUE=DATE-TIME:20210603T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/126
DESCRIPTION:Title: Fa
no varieties from homogeneous vector bundles\nby Enrico Fatighenti (Sa
pienza - Università di Roma) as part of ZAG (Zoom Algebraic Geometry) sem
inar\n\n\nAbstract\nThe idea of classifying Fano varieties using homogeneo
us vector bundles was behind Mukai's classification of prime Fano 3-folds.
In this talk\, we give a survey of some recent progress along the same li
nes\, including a biregular rework of the non-prime Mori-Mukai 3-folds cla
ssification and some examples of higher-dimensional Fano varieties with sp
ecial Hodge-theoretical properties.\n
LOCATION:https://researchseminars.org/talk/ZAG/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Borisov (Rutgers University)
DTSTART;VALUE=DATE-TIME:20210608T150000Z
DTEND;VALUE=DATE-TIME:20210608T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/127
DESCRIPTION:Title: Ex
plicit equations of surfaces of general type\nby Lev Borisov (Rutgers
University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract
\nI will talk about progress in finding equations of special surfaces of g
eneral type\, notably fake projective planes. This work was done over the
last several years\, in a series of joint papers with JongHae Keum\, Sai K
ee Yeung\, Enrico Fatighenti and Anders Buch.\n
LOCATION:https://researchseminars.org/talk/ZAG/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fumiaki Suzuki (UCLA Mathematics)
DTSTART;VALUE=DATE-TIME:20210610T160000Z
DTEND;VALUE=DATE-TIME:20210610T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/128
DESCRIPTION:Title: An
O-acyclic variety of even index\nby Fumiaki Suzuki (UCLA Mathematics)
as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nI will co
nstruct a family of Enriques surfaces parametrized by P^1 such that any mu
lti-section has even degree over the base P^1. Over the function field of
a complex curve\, this gives the first example of an O-acyclic variety (H^
i(X\,O)=0 for i>0) whose index is not equal to one\, and an affirmative an
swer to a question of Colliot-Thélène and Voisin. I will also discuss ap
plications to related problems\, including the integral Hodge conjecture a
nd Murre’s question on universality of the Abel-Jacobi maps. This is joi
nt work with John Christian Ottem.\n
LOCATION:https://researchseminars.org/talk/ZAG/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eveline Legendre (Institut de Mathématiques de Toulouse)
DTSTART;VALUE=DATE-TIME:20210615T110000Z
DTEND;VALUE=DATE-TIME:20210615T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/129
DESCRIPTION:Title: Va
luative stability for polarised varieties\nby Eveline Legendre (Instit
ut de Mathématiques de Toulouse) as part of ZAG (Zoom Algebraic Geometry)
seminar\n\n\nAbstract\nI will talk about a recent joint work with Ruadhai
Dervan where we introduced a notion of valuative stability for polarised
variety. This extends Fujita's valuative stability of Fano varieties. We s
how that valuative stability is equivalent to K-stability with respect to
test configurations with integral central fibre.\n
LOCATION:https://researchseminars.org/talk/ZAG/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Cascini (Imperial College London)
DTSTART;VALUE=DATE-TIME:20210617T160000Z
DTEND;VALUE=DATE-TIME:20210617T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/130
DESCRIPTION:Title: Bi
rational geometry of foliations on a complex threefold\nby Paolo Casci
ni (Imperial College London) as part of ZAG (Zoom Algebraic Geometry) semi
nar\n\n\nAbstract\nMany results in the classical minimal model program\, s
uch as the existence of flips and the base point free theorem\, admit a na
tural generalisation to the category of foliations defined over a complex
threefold. Other results\, instead\, seem to behave differently\, such as
existence of flops and canonical models. I will survey about some of the r
ecent progress in this direction. Joint work with C. Spicer.\n
LOCATION:https://researchseminars.org/talk/ZAG/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krishna Hanumanthu (Chennai Mathematical Institute)
DTSTART;VALUE=DATE-TIME:20210622T110000Z
DTEND;VALUE=DATE-TIME:20210622T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/131
DESCRIPTION:Title: Ra
tionality questions on Seshadri constants.\nby Krishna Hanumanthu (Che
nnai Mathematical Institute) as part of ZAG (Zoom Algebraic Geometry) semi
nar\n\n\nAbstract\nLet X be a projective variety and let L be an ample lin
e bundle on X. For a point x in X\, the Seshadri constant of L at x is the
infimum\, over all curves C passing through x\, of the ratios (L.C)/m\, w
here (L.C) denotes the intersection product of L and C and m is the multip
licity of C at x. These constants were defined by J.-P. Demailly in 1990
and they shed light on the local behaviour of L at x and even say somethin
g about the nature of L and X. An important question about Seshadri const
ants is whether they can be irrational. They are expected to be irrational
often\, even though currently no examples are known. In this talk\, we wi
ll focus on rational surfaces. We will discuss certain conjectures on line
ar systems of plane curves and show that Seshadri constants of some ample
line bundles are irrational if these conjectures are true. This talk is ba
sed on joint works with B. Harbourne\, \\L. Farnik\, J. Huizenga\, D. Schm
itz and T. Szemberg.\n
LOCATION:https://researchseminars.org/talk/ZAG/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Howard Nuer (Technion\, Israel Institute of Technology)
DTSTART;VALUE=DATE-TIME:20210624T110000Z
DTEND;VALUE=DATE-TIME:20210624T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/132
DESCRIPTION:Title: Th
e cohomology of the general stable sheaf on a K3 surface\nby Howard N
uer (Technion\, Israel Institute of Technology) as part of ZAG (Zoom Algeb
raic Geometry) seminar\n\n\nAbstract\nLet X be a K3 surface of Picard rank
one and degree 2n with ample generator H. Let M_H(v) be the moduli space
of Gieseker semistable sheaves on X with Mukai vector v. In this talk\, we
consider the weak Brill-Noether property for v\, namely that the general
sheaf in M_H(v) has at most one nonzero cohomology group. We show that g
iven any positive rank r\, there are only finitely many Mukai vectors of r
ank r failing weak Brill-Noether over all K3 surfaces of Picard rank one.
We discuss our algorithm for finding the potential counterexamples and dem
onstrate the utility of our approach by discussing how we were able to cla
ssify all such counterexamples up to rank 20 and calculate the cohomology
of the general sheaf in each case. Moreover\, for fixed rank r\, we give
sharp bounds on n\, d\, and a that guarantee that a Mukai vector v=(r\,dH\
,a) satisfies weak Brill-Noether. As a corollary\, we provide another pro
of of the classification of Ulrich bundles on K3 surfaces of Picard rank o
ne. In addition\, we discuss the question of when the general sheaf in M_H
(v) is globally generated. This joint work with Izzet Coskun and Kota Yosh
ioka makes crucial use of Bridgeland stability conditions and wall-crossin
g.\n
LOCATION:https://researchseminars.org/talk/ZAG/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Fernandez de Bobadilla (Basque Center for Applied Mathemati
cs)
DTSTART;VALUE=DATE-TIME:20210629T110000Z
DTEND;VALUE=DATE-TIME:20210629T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/133
DESCRIPTION:Title: Th
e Brasselet-Schurmann-Yokura conjecture for L-classes on singular varietie
s\nby Javier Fernandez de Bobadilla (Basque Center for Applied Mathema
tics) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nThe
Brasselet-Schurmann-Yokura conjecture predicts the equality between the Ho
dge L-class and the Goresky-MacPherson L-class for compact complex algebra
ic varieties that are rational homology manifolds. In this talk\, we give
two different proofs of this conjecture. The first proof is for projective
varieties\, and it is based on cubical hyperresolutions\, the Decompositi
on Theorem\, and classical Hodge theory. This is a joint work with I. Pall
ares. The second proof is for general compact algebraic varieties by using
the theory of mixed Hodge modules. This is a joint work with I. Pallares
and M. Saito.\n
LOCATION:https://researchseminars.org/talk/ZAG/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sheng Meng (Korea Institute for Advanced Study)
DTSTART;VALUE=DATE-TIME:20210701T110000Z
DTEND;VALUE=DATE-TIME:20210701T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/134
DESCRIPTION:Title: Au
tomorphism group and its Jordan property\nby Sheng Meng (Korea Institu
te for Advanced Study) as part of ZAG (Zoom Algebraic Geometry) seminar\n\
n\nAbstract\nA group is said to have Jordan property if there exists a Jor
dan constant J such that any finite subgroup has an abelian subgroup with
index bounded by J. I will survey known results for Jordan property on cer
tain automorphism groups and birational automorphism groups of varieties.
I will also explain our recent progress on automorphism groups of compact
spaces in Fujiki’s class C. This is a joint work with Fabio Perroni and
De-Qi Zhang.\n
LOCATION:https://researchseminars.org/talk/ZAG/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Taku Suzuki (Utsunomiya University)
DTSTART;VALUE=DATE-TIME:20210706T100000Z
DTEND;VALUE=DATE-TIME:20210706T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/135
DESCRIPTION:Title: Hi
gher order minimal families of rational curves on Fano manifolds\nby T
aku Suzuki (Utsunomiya University) as part of ZAG (Zoom Algebraic Geometry
) seminar\n\n\nAbstract\nThe purpose of my talk is to introduce the notion
of higher order minimal families of rational curves on Fano manifolds and
to explain two results concerning it. One is that Fano manifolds are cove
red by higher rational manifolds if their Chern characters satisfy some po
sitivity conditions. The other is a classification of embedded Fano manifo
lds covered by higher linear spaces.\n
LOCATION:https://researchseminars.org/talk/ZAG/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aline Zanardini (Leiden University)
DTSTART;VALUE=DATE-TIME:20210708T150000Z
DTEND;VALUE=DATE-TIME:20210708T160000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/136
DESCRIPTION:Title: St
ability of pencils of plane curves\nby Aline Zanardini (Leiden Univers
ity) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn th
is talk I will discuss some recent results on the problem of classifying p
encils of plane curves up to projective equivalence. We will see how the s
tability of a pencil is related to the stability of its generators\, to th
e log canonical threshold\, and to the multiplicities of a base point. In
particular\, I will present complete stability criteria for certain pencil
s of plane sextics called Halphen pencils of index two.\n
LOCATION:https://researchseminars.org/talk/ZAG/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zheng Zhang (ShanghaiTech)
DTSTART;VALUE=DATE-TIME:20210713T100000Z
DTEND;VALUE=DATE-TIME:20210713T110000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/137
DESCRIPTION:Title: Th
e moduli space of cubic surface pairs via the intermediate Jacobians of Ec
kardt cubic threefolds\nby Zheng Zhang (ShanghaiTech) as part of ZAG (
Zoom Algebraic Geometry) seminar\n\n\nAbstract\nWe study the moduli space
of pairs consisting of a smooth cubic surface and a transverse plane via a
period map. More specifically\, the construction associates to a cubic su
rface pair a so-called Eckardt cubic threefold which admits an involution\
, and the period map sends the pair to the anti-invariant part of the inte
rmediate Jacobian. Our main result is that the global Torelli theorem hold
s for the period map (in other words\, the period map is injective). The k
ey ingredients of the proof include a description of the anti-invariant pa
rt of the intermediate Jacobian as a Prym variety of a branched cover and
a detailed study of certain positive dimensional fibers of the correspondi
ng Prym map. This is joint work with S. Casalaina-Martin.\n
LOCATION:https://researchseminars.org/talk/ZAG/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicole Lemire (University of Western Ontario)
DTSTART;VALUE=DATE-TIME:20210715T160000Z
DTEND;VALUE=DATE-TIME:20210715T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/138
DESCRIPTION:Title: Co
dimension 2 cycles of classifying spaces of low-dimensional algebraic tori
\nby Nicole Lemire (University of Western Ontario) as part of ZAG (Zoo
m Algebraic Geometry) seminar\n\n\nAbstract\nLet T be an algebraic torus o
ver a field F\, and let CH^2(BT) be the Chow group of codimension 2 cycles
in its classifying space. Following work of Blinstein and Merkurjev on th
e structure of the torsion part of CH^2(BT)\, Scavia\, in a recent preprin
t\, found an example of an algebraic torus with non-trivial torsion in CH^
2(BT). In joint work with Alexander Neshitov\, we show computationally tha
t the group CH^2(BT) is torsion-free for all algebraic tori of dimension a
t most 5 and determine the conjugacy classes of finite subgroups of GL_6(Z
) which correspond to 6-dimensional tori with nontrivial torsion in CH^2(B
T). Some interesting properties of the structure of low-dimensional algebr
aic tori are involved.\n
LOCATION:https://researchseminars.org/talk/ZAG/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eiji Inoue (RIKEN iTHEMS)
DTSTART;VALUE=DATE-TIME:20210720T110000Z
DTEND;VALUE=DATE-TIME:20210720T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/139
DESCRIPTION:Title: Pe
relman's entropy and optimal degeneration\nby Eiji Inoue (RIKEN iTHEMS
) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nAlgebrai
c optimal degeneration of Fano variety along Kahler-Ricci flow was origina
lly constructed by Chen-Sun-Wang and was deepened by Dervan-Szekelyhidi\,
Han-Li and recent Blum-Liu-Xu-Zhuang. The degeneration is a substantial in
termediate for studying a Fano variety with Kahler-Ricci soliton appearing
in the Gromov-Hausdorff limit of Kahler-Ricci flow. The degeneration is c
haracterized by a valuation which maximizes `H-entropy' among all valuatio
ns. Motivated by these works\, I would like to explain my ongoing attempt
to optimal degeneration of polarized variety with respect to `mu-entropy'.
The mu-entropy appears in my study on mu-cscK metrics and muK-stability\,
which I introduced to understand cscK metrics and Kahler-Ricci soliton in
a unified way. Going deep into the story\, we encounter Perelman's entrop
y\, which turns out to be the origin of our story.\n
LOCATION:https://researchseminars.org/talk/ZAG/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Swarnava Mukhopadhyay (Tata Institute of Fundamental Research)
DTSTART;VALUE=DATE-TIME:20210722T110000Z
DTEND;VALUE=DATE-TIME:20210722T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/140
DESCRIPTION:Title: Hi
tchin connection for parabolic bundles\nby Swarnava Mukhopadhyay (Tata
Institute of Fundamental Research) as part of ZAG (Zoom Algebraic Geometr
y) seminar\n\n\nAbstract\nIn a fundamental paper in1990\, Hitchin consider
ed the space of non-abelian theta functions/conformal blocks/Verlinde spac
es from the view point of geometric-quantization (Konstant-Kirillov-Sourea
u) for the moduli space of principal bundles on a smooth projective curv
e. Hitchin found a flat projective connection that can be interpreted as i
dentification of these spaces via a parallel transport along a path joinin
g different curves in the Teichmuller space. In this talk\, we will discus
s a generalization of Hitchin's construction to the parabolic set-up. Name
ly we consider punctured curves and the moduli space of parabolic $G$ bund
les and produce a flat projective connection that identifies sections of p
arabolic determinant bundles as the puncture curve varies. This is a joint
work with Indranil Biswas and Richard Wentworth.\n
LOCATION:https://researchseminars.org/talk/ZAG/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenneth Ascher (Princeton University)
DTSTART;VALUE=DATE-TIME:20210727T160000Z
DTEND;VALUE=DATE-TIME:20210727T170000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/141
DESCRIPTION:Title: K-
stability and birational geometry of moduli spaces of quartic K3 surfaces<
/a>\nby Kenneth Ascher (Princeton University) as part of ZAG (Zoom Algebra
ic Geometry) seminar\n\n\nAbstract\nWe discuss various compactifications o
f moduli spaces of quartic K3 surfaces constructed using GIT\, hodge theor
y\, and K-stability. This is based on joint work with Kristin DeVleming an
d Yuchen Liu.\n
LOCATION:https://researchseminars.org/talk/ZAG/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anand Sawant (Tata Institute of Fundamental Research)
DTSTART;VALUE=DATE-TIME:20210729T110000Z
DTEND;VALUE=DATE-TIME:20210729T120000Z
DTSTAMP;VALUE=DATE-TIME:20210804T231253Z
UID:ZAG/142
DESCRIPTION:Title: Ne
ar-rationality properties of norm varieties\nby Anand Sawant (Tata Ins
titute of Fundamental Research) as part of ZAG (Zoom Algebraic Geometry) s
eminar\n\n\nAbstract\nThe standard norm varieties played a crucial role in
Voevodsky's proof of the Bloch-Kato conjecture. I will discuss various n
ear-rationality concepts for smooth projective varieties and describe know
n near-rationality results for standard norm varieties. I will then outli
ne an argument showing that a standard norm variety over a field of charac
teristic 0 is universally R-trivial after passing to the algebraic closure
of the base field. The talk is based on joint work with Chetan Balwe and
Amit Hogadi.\n
LOCATION:https://researchseminars.org/talk/ZAG/142/
END:VEVENT
END:VCALENDAR