BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Mikhail Ovcharenko (HSE)
DTSTART;VALUE=DATE-TIME:20200416T150000Z
DTEND;VALUE=DATE-TIME:20200416T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/1
DESCRIPTION:Title: Fano weighted complete intersections of large codimension\nby Mikha
il Ovcharenko (HSE) as part of Iskovskikh seminar\n\n\nAbstract\nLet $X$ b
e a smooth Fano variety. The index of $X$ is the largest natural number $i
_X$ such that the canonical class $K_X$ is divisible by $i_X$ in the Picar
d group of $X$. It is well known that $i_X \\le n(X) + 1$ for $n(X) = dim(
X)$.\n\nWe are going to consider smooth Fano weighted complete intersectio
ns over an algebraically closed field of characteristic zero. It is known
that\n$k(X) \\le n(X) + 1 - i_X$\nfor any such $X$\, where $k(X)$ is the c
odimension of $X$.\n\nLet us introduce new invariant $r(X) = n(X) - k(X) -
i_X + 1$.\nIn the talk I will outline what is known about smooth Fano wei
ghted complete intersection of given $r(X) = r_0$.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joaquín Moraga (Princeton University)
DTSTART;VALUE=DATE-TIME:20200422T150000Z
DTEND;VALUE=DATE-TIME:20200422T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/2
DESCRIPTION:Title: The local fundamental group of klt singularities\nby Joaquín Morag
a (Princeton University) as part of Iskovskikh seminar\n\n\nAbstract\nWe w
ill discuss some recent developments in the understanding of klt singulari
ties\,\nparticularly\, the Jordan property for the local fundamental group
. Then\, we will discuss how \na large local fundamental group reflects in
the geometry of the singularity. The approach\nto this question gives ris
e to some interesting conjectures about Fano type varieties with \nlarge f
inite abelian automorphisms.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Ottem (University of Oslo)
DTSTART;VALUE=DATE-TIME:20200430T150000Z
DTEND;VALUE=DATE-TIME:20200430T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/3
DESCRIPTION:Title: Tropical degenerations and stable rationality\nby John Ottem (Unive
rsity of Oslo) as part of Iskovskikh seminar\n\n\nAbstract\nI will explain
how tropical degenerations and birational specialization techniques can b
e used in rationality problems. In particular\, I will show that generic q
uartic fivefolds\, as well as many other complete intersections in project
ive space\, are stably irrational. This is joint work with Johannes Nicais
e.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arman Sarikyan (Moscow State University)
DTSTART;VALUE=DATE-TIME:20200504T150000Z
DTEND;VALUE=DATE-TIME:20200504T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/4
DESCRIPTION:Title: On Stable conjugacy of Finite Subgroups of the Plane Cremona Group\
nby Arman Sarikyan (Moscow State University) as part of Iskovskikh seminar
\n\n\nAbstract\nI will speak about linearization and stable linearization
of finite subgroups of the plane Cremona group. We will discuss an example
of nonlinerizable but stably linerizable group. Then I will classify all
linearizable and nonlinerizable groups and in some cases we will proof the
nonexistence of stable linearization.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Benoist (CNRS)
DTSTART;VALUE=DATE-TIME:20200507T150000Z
DTEND;VALUE=DATE-TIME:20200507T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/5
DESCRIPTION:Title: Intermediate Jacobians and rationality over arbitrary fields\nby Ol
ivier Benoist (CNRS) as part of Iskovskikh seminar\n\n\nAbstract\nClemens
and Griffiths have used intermediate Jacobians to show that smooth cubic t
hreefolds are irrational. In this talk\, I will explain how to extend the
Clemens-Griffiths method over arbitrary fields. As an application\, I will
show that a three-dimensional smooth complete intersection of two quadric
s over a field $\\mathbb k$ is $\\mathbb k$-rational if and only if it con
tains a line defined over $\\mathbb k$. This is joint work with Olivier Wi
ttenberg.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ignasi Mundet i Riera (University of Barselona)
DTSTART;VALUE=DATE-TIME:20200514T150000Z
DTEND;VALUE=DATE-TIME:20200514T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/6
DESCRIPTION:Title: Jordan and almost fixed point properties for topological manifolds\
nby Ignasi Mundet i Riera (University of Barselona) as part of Iskovskikh
seminar\n\n\nAbstract\nI will explain recent results on the Jordan propert
y for homeomorphism\ngroups that generalize most of the presently known re
sults about Jordan\ndiffeomorphism groups. A crucial ingredient in these r
esults is a recent \ntheorem of Csikós\, Pyber and Szabó. I will also ta
lk about the following\napplication. Let X be a compact topological manifo
ld\, possibly with boundary\,\nwith nonzero Euler characteristic. Then the
re exists a constant $C$ such\nthat for any continuous action of any finit
e group $G$ on $X$ there is a point\nin $X$ whose stabilizer has index in
$G$ not bigger than $C$.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Lesieutre (The Pennsylvania State University)
DTSTART;VALUE=DATE-TIME:20200521T150000Z
DTEND;VALUE=DATE-TIME:20200521T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/7
DESCRIPTION:Title: Pathologies of the volume function\nby John Lesieutre (The Pennsylv
ania State University) as part of Iskovskikh seminar\n\n\nAbstract\nThe "v
olume" of a line bundle $L$ on a projective variety is a measure of the gr
owth rate of the number of sections of its tensor powers $L^{\\otimes m}$.
I will describe two examples in which the behavior of this function near
the pseudoeffective boundary has unexpectedly complicated behavior\, and
discuss some implications for attempts to define a numerical analog of the
Iitaka dimension.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Batyrev (University of Tübingen)
DTSTART;VALUE=DATE-TIME:20200528T150000Z
DTEND;VALUE=DATE-TIME:20200528T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/8
DESCRIPTION:Title: Stringy Euler numbers of toric Calabi-Yau hypersurfaces\nby Victor
Batyrev (University of Tübingen) as part of Iskovskikh seminar\n\n\nAbstr
act\nThe talk is devoted to stringy\ninvariants of singular algebraic vari
eties\nand their applications in birational geometry\nand mirror symmetry.
Projective Calabi-Yau\nmodels of non-degenerate affine hypersurfaces in\n
algebraic torus provide simplest\nexamples of explicit combinatorial form
ulas\nfor stringy invariants. I explain some recent\nresults and open ques
tions motivated by different\nmirror symmetry constructions.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Trepalin (Steklov Mathematical Institute)
DTSTART;VALUE=DATE-TIME:20200604T150000Z
DTEND;VALUE=DATE-TIME:20200604T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/9
DESCRIPTION:Title: Birational permutations of projective plane (based on works of S.Cantat
and S.Asgarli\, K.Lai\, M.Nakahara and S.Zimmermann)\nby Andrey Trepa
lin (Steklov Mathematical Institute) as part of Iskovskikh seminar\n\n\nAb
stract\nLet us consider a projective plane over a finite field K. If a bir
ational transformation and its inverse are defined at each K-point\, then
this transformation defines a permutation of K-points. In the talk we disc
uss for which fields we can realize any permutation\, and for which not.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Louis Colliot-Thélène (Université Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20200611T150000Z
DTEND;VALUE=DATE-TIME:20200611T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/10
DESCRIPTION:Title: Zero-cycles on Del Pezzo surfaces\nby Jean-Louis Colliot-Thélène
(Université Paris-Saclay) as part of Iskovskikh seminar\n\n\nAbstract\nI
n 1974\, D. Coray showed that on a smooth cubic surface with a closed poin
t\nof degree prime to 3 there exists such a point of degree 1\, 4 or 10.\n
We show how a combination of generization\, specialisation\,\nBertini the
orems and large fields avoids considerations of special\ncases in his argu
ment. For del Pezzo surfaces of degree 2\, we give\nan analogue of Coray'
s result. For smooth cubic surfaces with a rational point\,\nwe show that
any zero-cycle of degree at least 10 is rationally equivalent to\nan effec
tive cycle. For smooth cubic surfaces without a rational point\,\nwe rela
te the question whether there exists a degree 3 point \nwhich is not on a
line to the question whether rational points are dense\non a del Pezzo sur
face of degree 1.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Gu
DTSTART;VALUE=DATE-TIME:20200618T073000Z
DTEND;VALUE=DATE-TIME:20200618T090000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/11
DESCRIPTION:Title: Surface fibrations with large equivariant automorphism groups\nby
Yi Gu as part of Iskovskikh seminar\n\n\nAbstract\nGiven a fibration $f: X
\\to C$ from a smooth projective surface $X$ to a smooth curve $C$ over an
arbitrary algebraically closed field $k$. The equivariant automorphism gr
oup is $$\\mathbb{E}(X/C):=\\{\\\,\\\,(\\tau\,\\sigma) \\\,\\\,|\\\,\\\, \
\tau\\in \\mathrm{Aut}_k(X)\, \\sigma\\in \\mathrm{Aut}_k(C)\,\\\,\\\,\\\,
f\\circ \\tau =\\sigma\\circ f\\\,\\\, \\}$$\nwith natural composition l
aw.\n $$\n\\xymatrix{ X\\ar[rr]_\\sim^\\tau \\ar[d]_f&& X \\ar[d]^f\\\\\nC
\\ar[rr]_\\sim^\\sigma && C\n}\n$$\nThis group is an important invariant
of the fibration $f$ and sometimes that of the surface $X$. In this talk\,
we will give a classification of those relatively minimal surface fibrati
ons whose equivariant automorphism group $\\mathbb{E}(X/C)$ is infinite. A
s an application\, we will also discuss the Jordan property of the automor
phism group of a minimal surface of Kodaira dimension one.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caucher Birkar (University of Cambridge)
DTSTART;VALUE=DATE-TIME:20200625T130000Z
DTEND;VALUE=DATE-TIME:20200625T143000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/12
DESCRIPTION:Title: On non-rationality of degenerations of del Pezzo surfaces\nby Cauc
her Birkar (University of Cambridge) as part of Iskovskikh seminar\n\n\nAb
stract\nIt is well-known that a degeneration of a del Pezzo surface may no
t be rational. A natural question is how far can it be from being rational
. In this talk I will describe some recent results in this direction\, in
joint work with Konstantin Loginov.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Hassett (Brown University)
DTSTART;VALUE=DATE-TIME:20200702T150000Z
DTEND;VALUE=DATE-TIME:20200702T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/13
DESCRIPTION:Title: Symbols\, birational geometry\, and computations\nby Brendan Hasse
tt (Brown University) as part of Iskovskikh seminar\n\n\nAbstract\nWe are
interested in $G$-birational equivalence of varieties where $G$ is a \nfin
ite group. Kontsevich-Tschinkel and Kresch-Tschinkel have developed \nsymb
ol formalism to construct invariants that show rich internal \nstructure.
We present examples of their computation in a number of \nsituations.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanni Mongardi (Bologna University)
DTSTART;VALUE=DATE-TIME:20200709T150000Z
DTEND;VALUE=DATE-TIME:20200709T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/14
DESCRIPTION:Title: IHS Manifolds: Automorphisms\, Kahler cones and related questions\
nby Giovanni Mongardi (Bologna University) as part of Iskovskikh seminar\n
\n\nAbstract\nAfter a (dramatically brief) introduction on IHS or Hyperkä
hler\nmanifolds\, we will\nsurvey several results on the shape of their K
ähler cones and related\ncones in the projective setting (ample\, movable
) and a\nBoucksom-Zarisky decomposition for divisors. Then\, we sketch how
these\nproperties can be used to describe automorphisms of IHS manifolds.
\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Tschinkel (Courant Institute of Mathematical Sciences)
DTSTART;VALUE=DATE-TIME:20200917T150000Z
DTEND;VALUE=DATE-TIME:20200917T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/15
DESCRIPTION:Title: Equivariant birational types\nby Yuri Tschinkel (Courant Institute
of Mathematical Sciences) as part of Iskovskikh seminar\n\n\nAbstract\nI
will discuss new invariants in equivariant birational geometry (joint with
B. Hassett and A. Kresch).\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Muhammad Imran Qureshi (KFUPM)
DTSTART;VALUE=DATE-TIME:20201015T150000Z
DTEND;VALUE=DATE-TIME:20201015T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/16
DESCRIPTION:Title: Fano 4-folds in weighted Grassmannians\nby Muhammad Imran Qureshi
(KFUPM) as part of Iskovskikh seminar\n\n\nAbstract\nA weighted flag varie
ty is a weighted projective analog of the usual flag variety. In this talk
\, I will provide an introduction and motivation behind the subject of wei
ghted flag varieties\, with particular emphasis on the first non-trivial c
ase of weighted Grassmannians. I aim to show that how one may use them as
ambient varieties to construct interesting classes of algebraic varieties
(Fano\, Calabi-Yau\, etc)\, which are important from the point of view of
the classification of algebraic varieties. As an application\, I will pr
esent some new deformation families of smooth Fano 4-folds of index 1.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Constantin Loginov (HSE)
DTSTART;VALUE=DATE-TIME:20201029T150000Z
DTEND;VALUE=DATE-TIME:20201029T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/17
DESCRIPTION:Title: Maximal log Fano pairs as generalized Bott towers\nby Constantin L
oginov (HSE) as part of Iskovskikh seminar\n\n\nAbstract\nLog Fano varieti
es are natural generalizations of Fano varieties. They\nare defined as pai
rs $(X\, D)$ such that $-K_X-D$ is ample and $D$ is a\ndivisor called a bo
undary. We consider the case of smooth projective X\nand reduced divisor $
D$ with simple normal crossings. Such pairs were\nstudied by H. Maeda\, Ta
kao and Kento Fujita\, and others. If in the\nabove definition we put $D =
0$ then we recover the classical definition\nof a Fano variety. We will s
tudy the opposite case of 'large enough'\nboundary divisor $D$. More preci
sely\, we will show that if $D$ has maximal\npossible number of components
(such log Fano pairs we call maximal)\nthen the geometry of X\, including
the Mori cone and extremal\ncontractions\, can be explicitly described. I
t turns out that such\npairs $(X\, D)$ are toric and moreover\, $X$ admits
the structure of a\ngeneralized Bott tower. This means that $X$ is an ite
rated projective\nbundle over a point. If time permits\, we will discuss h
ow maximal log\nFano pairs are related to semistable degenerations of Fano
varieties.\nThe talk is based on a joint work with J. Moraga.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudia Stadlmayr (Technische Universität München)
DTSTART;VALUE=DATE-TIME:20201112T150000Z
DTEND;VALUE=DATE-TIME:20201112T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/18
DESCRIPTION:Title: Which rational double points occur on del Pezzo surfaces?\nby Clau
dia Stadlmayr (Technische Universität München) as part of Iskovskikh sem
inar\n\n\nAbstract\nCanonical surface singularities\, also called rational
double points (RDPs)\, can be classified according to their dual resoluti
on graphs\, which are Dynkin diagrams of types A\, D\, and E. Whereas in c
haracteristic different from 2\, 3\, and 5\, rational double points are "t
aut"\, that is\, they are uniquely determined by their dual resolution gra
ph\, this is not necessarily the case in small characteristics. To such no
n-taut RDPs Artin assigned a coindex distinguishing the ones with the same
resolution graph in terms of their deformation theory.\n\nIn 1934\, Du Va
l determined all configurations of rational double points that can appear
on complex RDP del Pezzo surfaces. In order to extend Du Vals work to posi
tive characteristic\, one has to determine the Artin coindices to distingu
ish the non-taut rational double points that occur.\n\nIn this talk\, we w
ill answer the question "Which rational double points (and configurations
of them) occur on del Pezzo surfaces?" for all RDP del Pezzo surfaces in a
ll characteristics. This will be done by first reducing the problem to RDP
del Pezzo surfaces of degree 1 and then exploiting their connection to (W
eierstraß models of) rational (quasi-)elliptic surfaces.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elana Kalashnikov (Harvard\, HSE)
DTSTART;VALUE=DATE-TIME:20201126T150000Z
DTEND;VALUE=DATE-TIME:20201126T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/19
DESCRIPTION:Title: Mirror symmetry and quiver flag varieties\nby Elana Kalashnikov (H
arvard\, HSE) as part of Iskovskikh seminar\n\n\nAbstract\nQuiver flag var
ieties are a generalization of type A flag varieties\, first introduced by
Alastair Craw. They are natural ambient spaces\, and play a special role
in the Fano classification program\, where mirror constructions for these
varieties are of particular interest. I'll survey some of the different mi
rror constructions available for Grassmannians - via toric degenerations\,
quantum cohomology\, and the Abelian/non-Abelian correspondence - and dis
cuss some of the work generalizing these constructions to quiver flag vari
eties.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Svaldi (EPFL)
DTSTART;VALUE=DATE-TIME:20201203T150000Z
DTEND;VALUE=DATE-TIME:20201203T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/20
DESCRIPTION:Title: On the boundedness of Calabi--Yau elliptic fibrations\nby Roberto
Svaldi (EPFL) as part of Iskovskikh seminar\n\n\nAbstract\nOne of the main
goals in Algebraic Geometry is to classify varieties.\nThe minimal model
program (MMP) is an ambitious program that aims to realize this goal\, fro
m the point of view of birational geometry\, that is\, we are free to modi
fy the structure of a given variety along closed subsets to improve its ge
ometric features.\nAccording to the MMP\, there are 3 building blocks in t
he birational classification of algebraic varieties: Fano varieties\, Cal
abi-Yau varieties\, and varieties of general type. One important question
\, that is needed to further investigate the classification process\, is w
hether or not varieties in these 3 classes have finitely many deformation
types (a property called boundedness).\nOur understanding of the boundedne
ss of Fano varieties and varieties of general type is quite solid but Cal
abi-Yau varieties are still quite elusive. In this talk\, I will discuss r
ecent results on the boundedness of elliptic Calabi-Yau varieties\, whic
h are the most relevant in physics.\nAs a consequence\, we obtain that the
re are finitely many possibilities for the Hodge diamond of such manifolds
.\nThis is joint work with C. Birkar and G. Di Cerbo.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Shinder (The University of Sheffield)
DTSTART;VALUE=DATE-TIME:20201210T150000Z
DTEND;VALUE=DATE-TIME:20201210T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/21
DESCRIPTION:Title: Two-dimensional birational geometry and factorization centers\nby
Evgeny Shinder (The University of Sheffield) as part of Iskovskikh seminar
\n\n\nAbstract\nUsing results of Manin-Iskovskikh on classification of geo
metrically rational surfaces over a perfect field\, and results of Iskovsk
ikh on classification of links between such surfaces\, I will explain the
proof for uniqueness of factorization centers in dimension two. Explicitly
\, the result is that the sequence of centers blown up and blown down\, fo
r any birational isomorphism $\\phi: X\\to Y$ is independent of $\\phi$.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Höring (Université de Nice Sophia-Antipolis)
DTSTART;VALUE=DATE-TIME:20210211T150000Z
DTEND;VALUE=DATE-TIME:20210211T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/22
DESCRIPTION:Title: Fano manifolds with big tangent bundle that are covered by ``lines''\nby Andreas Höring (Université de Nice Sophia-Antipolis) as part of I
skovskikh seminar\n\n\nAbstract\nBy definition the anticanonical bundle of
a Fano manifold $X$ is ample\, but in general the tangent bundle $T_X$ do
es not have any nice properties.\nIn fact\, recent examples obtained in jo
int work with Jie Liu and Feng Shao indicate that the tangent bundle is al
most never big. Unfortunately so far we do not have many tools to study th
is property in an abstract setting. In this talk I will speak about work i
n progress with Jie Liu where we tackle the first case\, i.e. when $T_X$ i
s big and $X$ admits a family of minimal rational curves of degree two.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksey Golota (HSE)
DTSTART;VALUE=DATE-TIME:20210204T150000Z
DTEND;VALUE=DATE-TIME:20210204T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/23
DESCRIPTION:Title: Filtrations\, admissible flags and delta-invariants\nby Aleksey Go
lota (HSE) as part of Iskovskikh seminar\n\n\nAbstract\nDelta-invariant of
a Fano variety is a numerical invariant characterizing uniform K-stabilit
y. This invariant is defined using log canonical thresholds of basis-type
divisors. I am going to describe an «inductive» way to compute and estim
ate delta invariants for various examples of Fano varieties\, recently pro
posed by Ahmadinezhad and Zhuang.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valery Lunts (University of Indiana)
DTSTART;VALUE=DATE-TIME:20210218T150000Z
DTEND;VALUE=DATE-TIME:20210218T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/24
DESCRIPTION:Title: Thick finitely generated subcategories on affine schemes and curves\nby Valery Lunts (University of Indiana) as part of Iskovskikh seminar\n
\n\nAbstract\nI will report on three joint papers with Alexey Elagin.\nWe
study thick subcategories of derived categories $D^b(cohX)$\,\nin case $X$
is an affine scheme or a smooth projective curve. \nIn some cases we obt
ain a complete classification. Also some\nsurprising phenomena occur.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jungkai A. Chen (National Taiwan University)
DTSTART;VALUE=DATE-TIME:20210311T150000Z
DTEND;VALUE=DATE-TIME:20210311T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/25
DESCRIPTION:Title: Threefolds of general type fibered by surfaces with small volume\n
by Jungkai A. Chen (National Taiwan University) as part of Iskovskikh semi
nar\n\n\nAbstract\nIn birational classification theory\, it is interesting
to study the distribution and relations of birational invariants. Also\,
it is interesting to characterize those varieties with extremal invariants
. \nIn this talk\, we are going to work on threefolds of general type fibe
red by surfaces with small volume. \nBy combining the techniques of geomet
ry of linear systems and minimal model theory\, one can have quite explici
t description of such kinds of threefolds. \nWe will show applications to
the study of Noether type inequality\, Severi type inequality and threefol
ds with minimal volume.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksey Golota (HSE)
DTSTART;VALUE=DATE-TIME:20210318T150000Z
DTEND;VALUE=DATE-TIME:20210318T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/26
DESCRIPTION:Title: Filtrations\, admissible flags and delta-invariants\nby Aleksey Go
lota (HSE) as part of Iskovskikh seminar\n\n\nAbstract\nDelta-invariant of
a Fano variety is a numerical invariant characterizing uniform K-stabilit
y. This invariant is defined using log canonical thresholds of basis-type
divisors. I am going to describe an «inductive» way to compute and estim
ate delta invariants for various examples of Fano varieties\, recently pro
posed by Ahmadinezhad and Zhuang.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Petracci (Freie Universität Berlin)
DTSTART;VALUE=DATE-TIME:20210401T150000Z
DTEND;VALUE=DATE-TIME:20210401T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/27
DESCRIPTION:Title: Toric geometry and singularities on K-moduli\nby Andrea Petracci (
Freie Universität Berlin) as part of Iskovskikh seminar\n\n\nAbstract\nAn
immediate consequence of Kodaira-Akizuki-Nakano vanishing is that smooth
Fano varieties have unobstructed deformations. The same holds for singular
Fano varieties with mild singularities and small dimension. In this talk
I will show how to use the combinatorics of lattice polytopes to construct
examples of K-polystable toric Fano varieties with obstructed deformation
s\, dimension at least 3\, and canonical singularities. This produces sing
ularities (even reducible / non-reduced / non-Cohen-Macaulay) on K-moduli
stacks and K-moduli spaces of Fano varieties (which were recently construc
ted using K-stability). This is joint work with Anne-Sophie Kaloghiros.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weichung Chen (Steklov Mathematical Institute)
DTSTART;VALUE=DATE-TIME:20210325T150000Z
DTEND;VALUE=DATE-TIME:20210325T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/28
DESCRIPTION:Title: Bounded Complements for ϵ-lc generalized Fano Pairs\nby Weichung
Chen (Steklov Mathematical Institute) as part of Iskovskikh seminar\n\n\nA
bstract\nWe show the existence of strong $(\\epsilon\,n\,Γ)$-complements
for $\\epsilon$-lc generalized Fano pairs with coefficients of boundaries
in a fixed DCC set\, for any non-negative real number $\\epsilon$\, given
a certain ACC (ascending chain condition) for generalized $\\epsilon$-log
canonical threshold. This is a generalization combining Filipazzi-Moraga's
result in 2018 and Han-Liu-Shokurov's result in 2019\, which are based on
Birkar's construction in 2016. This is a joint work with Y. Gongyo and Y.
Nakamura.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikon Kurnosov (HSE\, UCL)
DTSTART;VALUE=DATE-TIME:20210408T150000Z
DTEND;VALUE=DATE-TIME:20210408T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/29
DESCRIPTION:Title: On Bogomolov theorem of classification of VII_0 surfaces\nby Nikon
Kurnosov (HSE\, UCL) as part of Iskovskikh seminar\n\n\nAbstract\nI will
talk about the classification of VII_0 surfaces\, in particular about idea
s of Bogomolov\, and Teleman's work\, who has made a complete classificati
on. Time permits we will talk about bottlenecks of Bogomolov's approach.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingjun Han (John Hopkins University)
DTSTART;VALUE=DATE-TIME:20210429T150000Z
DTEND;VALUE=DATE-TIME:20210429T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/30
DESCRIPTION:Title: Shokurov's conjecture on conic bundles with canonical singularities\nby Jingjun Han (John Hopkins University) as part of Iskovskikh seminar\
n\n\nAbstract\nA conic bundle is a contraction $X\\to Z$ between normal va
rieties of relative dimension $1$ such that the anit-canonical divisor is
relatively ample. In this talk\, I will prove a conjecture of Shokurov whi
ch predicts that\, if $X\\to Z$ is a conic bundle such that $X$ has canoni
cal singularities\, then base variety $Z$ is always $\\frac{1}{2}$-lc\, an
d the multiplicities of the fibers over codimension $1$ points are bounded
from above by $2$. Both values $\\frac{1}{2}$ and $2$ are sharp. This is
a joint work with Chen Jiang and Yujie Luo.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Loginov (Steklov Mathematical Institute)
DTSTART;VALUE=DATE-TIME:20210415T150000Z
DTEND;VALUE=DATE-TIME:20210415T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/31
DESCRIPTION:Title: A finiteness theorem for elliptic Calabi-Yau threefolds\nby Konsta
ntin Loginov (Steklov Mathematical Institute) as part of Iskovskikh semina
r\n\n\nAbstract\nCalabi-Yau varieties are generalizations of elliptic curv
es and K3\nsurfaces. From the point of view of algebraic geometry\, the qu
estion\nof boundedness of such varieties seems interesting. Following the
work\nof Mark Gross\, we prove that up to birational equivalence there are
\nonly finitely many families of 3-dimensional Calabi-Yau varieties that\n
satisfy certain conditions. More precisely\, singularities should be\nterm
inal and factorial\, and the given variety should admit a fibration\ninto
elliptic curves over a rational surface.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Rybakov (IITP)
DTSTART;VALUE=DATE-TIME:20210422T140000Z
DTEND;VALUE=DATE-TIME:20210422T153000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/32
DESCRIPTION:Title: Algebraic varieties over function fields and good towers of curves ove
r finite fields\nby Sergey Rybakov (IITP) as part of Iskovskikh semina
r\n\n\nAbstract\nGiven a smooth algebraic variety over a function field we
can construct a tower of algebraic curves (or\, equivalently\, a tower of
function fields). We say that the tower is good if the limit of the numbe
r of points on a curve divided by genus is positive. For example\, the gen
eric fiber of the Legendre family of elliptic curves gives a good (and opt
imal) tower over $F_{p^2}$. I will speak on good towers coming from K3 sur
faces.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Ovcharenko (HSE)
DTSTART;VALUE=DATE-TIME:20210527T150000Z
DTEND;VALUE=DATE-TIME:20210527T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/33
DESCRIPTION:Title: On Dolgachev--Nikulin Duality for Fibers of Landau--Ginzburg Models of
Smooth Fano Threefolds\nby Mikhail Ovcharenko (HSE) as part of Iskovs
kikh seminar\n\n\nAbstract\nMirror Symmetry corresponds to Fano varieties
certain one-dimensional families which are called Landau--Ginzburg models.
Elements of these families are expected to be Calabi--Yau varieties mirro
r dual to anticanonical sections of Fano varieties. In the three-dimension
al case one of the forms of Mirror Symmetry conjecture is provided by Dolg
achev--Nikulin duality of K3 surfaces. This conjecture was proved by Ilten
--Lewis--Przyjalkowski in the case of Picard rank 1. In the talk we will d
iscuss the obtained results for Picard rank 2.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Kuznetsova (HSE\, Ecole Polytechique)
DTSTART;VALUE=DATE-TIME:20210916T150000Z
DTEND;VALUE=DATE-TIME:20210916T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/34
DESCRIPTION:Title: Semi-continuity of dynamical degrees\nby Alexandra Kuznetsova (HSE
\, Ecole Polytechique) as part of Iskovskikh seminar\n\n\nAbstract\nTo any
birational automorphism we can associate its dynamical degree. This is a
number characterising the growth of any ample class under iteration of the
automorphism. If the automorphism is regular\, then its dynamical degree
equals the absolute value of the greatest eigenvalue of the action of the
inverse image on the Neron-Severi group of the variety.\nIf we fix a fami
ly of birational automorphisms\, then the dynamical degree defines a funct
ion on the base of the family. I am going to tell the proof of Xie Junyi's
theorem that in the case of a family of surface birational automorphisms
this function is lower semi-continuous.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Litt (University of Georgia)
DTSTART;VALUE=DATE-TIME:20210923T150000Z
DTEND;VALUE=DATE-TIME:20210923T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/35
DESCRIPTION:Title: Arithmetic representations and non-commutative Siegel linearization\nby Daniel Litt (University of Georgia) as part of Iskovskikh seminar\n\
n\nAbstract\nI'll explain joint work with Borys Kadets\, explaining how to
prove the following theorem. Let $X$ be a curve over a finitely generated
field $k$\, and let $\\ell$ be a prime different from the characteristic
of $k$. Then there exists $N=N(X\,\\ell)$ such that any semisimple arithme
tic representation of $\\pi_1(X_{\\bar k})$ into $GL_n(\\overline{\\mathbb
{Z}_\\ell})$\, which is trivial mod $\\ell^N$\, is in fact trivial. This e
xtends previous work of mine from characteristic zero to all characteristi
cs. The main new idea is to introduce techniques from dynamics\; in partic
ular a non-commutative version of Siegel's linearization theorem. For exam
ple\, this gives restrictions on the possible torsion subgroups of abelian
varieties over function fields. I'll also explain some related joint work
in progress with Eric Katz on $\\ell$-adic analogues of non-Abelian Hodge
theory.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Daurtseva (https://research.nsu.ru/en/persons/ndaurtseva)
DTSTART;VALUE=DATE-TIME:20210930T150000Z
DTEND;VALUE=DATE-TIME:20210930T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/36
DESCRIPTION:Title: On almost Hermitian structures on 6-dimensional manifolds\nby Nata
lia Daurtseva (https://research.nsu.ru/en/persons/ndaurtseva) as part of I
skovskikh seminar\n\n\nAbstract\nSix-dimensional case is special in geomet
ry of almost Hermitian manifolds.\nThis is due to the existence of a well-
known Hopf problem on a 6-sphere\,\nthe properties of nearly Kaehler manif
olds\, and a number of other reasons.\nI’ll talk about some questions an
d progresses in almost Hermitian geometry\,\nin particular\, about the pro
perties of almost Hermitian structures of cohomogeneity 1 on a 6-sphere.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annalisa Grossi (https://annalisagrossi92.wixsite.com/home)
DTSTART;VALUE=DATE-TIME:20211007T150000Z
DTEND;VALUE=DATE-TIME:20211007T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/37
DESCRIPTION:Title: Induced nonsymplectic automorphisms on manifolds of OG6 type\nby A
nnalisa Grossi (https://annalisagrossi92.wixsite.com/home) as part of Isko
vskikh seminar\n\n\nAbstract\nIn 2000 O'Grady introduced a new example of
hyperkaehler manifolds\nin dimension six as the symplectic resolution of a
certain fiber of a moduli space\nof sheaves on an abelian surface. In thi
s talk we give you a criterion to determine\nwhen a birational transformat
ion of an O'Grady six type manifold is induced by\nan automorphism of the
abelian surface. Using the lattice theoretic classi\ncation\nof nonsymplec
tic automorphisms of O'Grady's sixfolds we give an application of\nthis cr
iterion to detect when an automorphism is induced.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Vikulova (https://www.hse.ru/org/persons/401585497)
DTSTART;VALUE=DATE-TIME:20211014T150000Z
DTEND;VALUE=DATE-TIME:20211014T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/38
DESCRIPTION:Title: Enriques varieties\nby Anastasia Vikulova (https://www.hse.ru/org/
persons/401585497) as part of Iskovskikh seminar\n\n\nAbstract\nIn this ta
lk we will discuss generalizations of Enriques surfaces (so called Enrique
s varieties) and construct all examples of such varieties\, which are know
n today.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Bot (University of Basel)
DTSTART;VALUE=DATE-TIME:20211111T150000Z
DTEND;VALUE=DATE-TIME:20211111T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/40
DESCRIPTION:Title: A smooth complex rational affine surface with uncountably many nonisom
orphic real forms\nby Anna Bot (University of Basel) as part of Iskovs
kikh seminar\n\n\nAbstract\nA real form of a complex algebraic variety $X$
is a real algebraic variety whose complexification is isomorphic to $X$.
Up until recently\, it was known that many families of complex varieties h
ave a finite number of nonisomorphic real forms. In 2019\, Lesieutre const
ructed an example of a projective variety of dimension six with infinitely
many\, and now\, Dinh\, Oguiso and Yu found a projective rational surface
with infinitely many as well. In this talk\, I’ll present the first exa
mple of a rational affine surface having uncountably many nonisomorphic re
al forms. The first example with infinitely countably many real forms on a
n affine rational variety is due to Dubouloz\, Freudenberg and Moser-Jausl
in.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Tuzhilin (MSU)
DTSTART;VALUE=DATE-TIME:20211125T150000Z
DTEND;VALUE=DATE-TIME:20211125T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/41
DESCRIPTION:Title: Symmetries of Gromov-Hausdorff Distance\nby Alexey Tuzhilin (MSU)
as part of Iskovskikh seminar\n\n\nAbstract\nThe famous Gromov-Hausdorff d
istance measures the similarity degree of metric spaces. Since it both sat
isfies the triangle inequality and vanishes for isometric spaces\, it indu
ces correctly a correspondent distance on isometry classes of metric space
s. The collection of all such classes form a proper class in terms of Von
Neumann–Bernays–Gödel set theory. We call such proper class by Gromov
-Hausdorff class and denote it as GH. The main question for the talk is to
discuss what are the isometric mappings (local and global) of GH. One of
the most investigated part of GH is the Gromov-Hausdorff space M consistin
g of all non-empty compact metric spaces (considered up to isometry).\n\nW
e start with a sketch of Ivanov-Tuzhilin's correction of the "George Lowth
er" proof (perhaps "George Lowther" is a pseudonym) that the isometry grou
p of M is trivial. Then we discuss some local isometries of M: it turns ou
t that there are a lot of them. At last\, we formulate some conjectures co
ncerning the whole Gromov-Hausdorff class GH.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Avilov (HSE)
DTSTART;VALUE=DATE-TIME:20211021T150000Z
DTEND;VALUE=DATE-TIME:20211021T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/42
DESCRIPTION:Title: G-birationally rigid del Pezzo varieties of degree 2\nby Artem Avi
lov (HSE) as part of Iskovskikh seminar\n\n\nAbstract\nIn this talk we wil
l classify nodal non-$\\mathbb Q$-factorial quartic double solids with big
enough automorphism group such that there are no simple equivariant links
with another Mori fibrations.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Piskunov (HSE)
DTSTART;VALUE=DATE-TIME:20211027T140000Z
DTEND;VALUE=DATE-TIME:20211027T153000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/43
DESCRIPTION:Title: Symmetric powers of Severi-Brauer varieties\nby Alexei Piskunov (H
SE) as part of Iskovskikh seminar\n\n\nAbstract\nA Severi-Brauer variety o
ver a field $k$ is an algebraic variety $X/k$ that becomes isomorphic to t
he projective space $\\mathbb P^n$ after the base change to a separable cl
osure $k^{sep}$. I will show that $(n+1)$-th symmetric power of any $n$-di
mensional Severi-Brauer varietiy is rational. We will also study some fact
s about their arbitrary symmetric powers and Grassmanians. The talk is due
to the article of János Kollár and is going to be elementary (only some
basic facts from algebraic geometry will be used).\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Loginov (Steklov Mathematical Institute)
DTSTART;VALUE=DATE-TIME:20211118T150000Z
DTEND;VALUE=DATE-TIME:20211118T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/44
DESCRIPTION:Title: Termination of flips and fundamental groups (after Joaquín Moraga)\nby Konstantin Loginov (Steklov Mathematical Institute) as part of Iskov
skikh seminar\n\n\nAbstract\nWe will talk about the connection between top
ology of singularities of\nalgebraic varieties and the following important
conjectures in the\nminimal model program: termination of flips conjectur
e and the\nconjecture on boundedness of minimal log discrepancies. In\npa
rticular\, we will formulate the boundedness conjecture for the\nregional
fundamental group\, which is proven by Joaquín for some\nclasses of singu
larities. Also\, we will show that this conjecture\nimplies termination of
flips for klt pairs in dimension 4.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Ovcharenko (Steklov Mathematical Institute)
DTSTART;VALUE=DATE-TIME:20211202T150000Z
DTEND;VALUE=DATE-TIME:20211202T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/45
DESCRIPTION:Title: Varieties of general type with the smallest known volume (after Esser-
-Totaro--Wang)\nby Mikhail Ovcharenko (Steklov Mathematical Institute)
as part of Iskovskikh seminar\n\n\nAbstract\nIn the talk we will construc
t smooth projective varieties of general type with the smallest known volu
me and others with the most known vanishing plurigenera.\n\nThe optimal vo
lume bound is expected to decay doubly exponentially with dimension. The c
onstructed examples will have the required asymptotic.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ronald van Luijk (Universiteit Leiden)
DTSTART;VALUE=DATE-TIME:20211209T150000Z
DTEND;VALUE=DATE-TIME:20211209T163000Z
DTSTAMP;VALUE=DATE-TIME:20211209T062400Z
UID:Iskovskikh/46
DESCRIPTION:Title: Density of rational points on a family of Del Pezzo surfaces of degree
1\nby Ronald van Luijk (Universiteit Leiden) as part of Iskovskikh se
minar\n\n\nAbstract\nDel Pezzo surfaces are geometrically among the easies
t surfaces. They have a degree between 1 and 9\, and the lower the degree\
, the more complicated the surface. Those of degree 3 are the famous cubic
surfaces containing 27 lines. The arithmetic of Del Pezzo surfaces\, howe
ver\, is much less understood. It is conjectured that on every Del Pezzo s
urface over a number field k with at least one k-rational point\, the set
of k-rational points is automatically dense. This has been proved for all
Del Pezzo surfaces of degree at least 3\, most of degree 2\, but only few
of degree 1\, which is the case we will discuss. These surfaces have a nat
ural elliptic fibration. We will prove for a large family of these surface
s that the set of rational points is Zariski dense if and only if there is
at least one fiber (satisfying very mild conditions) that contains infini
tely many rational points. This is joint work with Wim Nijgh\, based on wo
rk of Rosa Winter and Julie Desjardins.\n
LOCATION:https://researchseminars.org/talk/Iskovskikh/46/
END:VEVENT
END:VCALENDAR