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SUMMARY:Simon Felten (JGU Mainz)
DTSTART;VALUE=DATE-TIME:20210412T141500Z
DTEND;VALUE=DATE-TIME:20210412T154500Z
DTSTAMP;VALUE=DATE-TIME:20230208T081231Z
UID:algebraic_geometry_FU/1
DESCRIPTION:Title: The logarithmic Bogomolov-Tian-Todorov theorem\nby Simon
Felten (JGU Mainz) as part of Algebraic geometry Freie Universität Berli
n\n\n\nAbstract\nA variety V with only normal crossing singularities does
only admit a semistable smoothing if it is d-semistable\, but this conditi
on is not sufficient. However\, d-semistability is sufficient to endow V w
ith the structure of a logarithmically smooth log morphism to the standard
log point\; then constructing a semistable smoothing becomes essentially
equivalent to constructing an infinitesimal log smooth deformation of V up
to any order. Morally\, but not in practice\, this is achieved by a logar
ithmic Bogomolov--Tian--Todorov Theorem---the unobstructedness of the log
smooth deformation functor---in case that V is Calabi--Yau. In view of Iac
ono--Manetti's algebraic proof of the classical BTT theorem\, we need a dg
la which controls the log smooth deformation functor. However\, the straig
htforward approach fails for rather obvious reasons. Instead\, we study de
formations of the Gerstenhaber algebra of log polyvector fields. On the on
e hand\, this yields the sought-after replacement of the dgla. On the othe
r hand\, this yields by results of Chan--Leung--Ma a weaker unobstructedne
ss result\; nonetheless\, it is sufficient to construct semistable smoothi
ngs and implies---by local algebra---the full logarithmic Bogomolov--Tian-
-Todorov Theorem.\n
LOCATION:https://researchseminars.org/talk/algebraic_geometry_FU/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mattia Talpo (University of Pisa)
DTSTART;VALUE=DATE-TIME:20210419T141500Z
DTEND;VALUE=DATE-TIME:20210419T154500Z
DTSTAMP;VALUE=DATE-TIME:20230208T081231Z
UID:algebraic_geometry_FU/2
DESCRIPTION:Title: Topological realization over C((t)) via Kato-Nakayama spaces
\nby Mattia Talpo (University of Pisa) as part of Algebraic geometry F
reie Universität Berlin\n\n\nAbstract\nI will talk about some joint work
with Piotr Achinger\, about a “Betti realization” functor for varietie
s over the formal punctured disk Spec C((t))\, i.e. defined by polynomials
with coefficients in the field of formal Laurent series in one variable o
ver the complex numbers. We give two constructions producing the same resu
lt\, one of them (the one that I'll actually talk about) via “good model
s” over the power series ring C[[t]] and the “Kato-Nakayama” constru
ction in logarithmic geometry\, that I will review during the talk.\n
LOCATION:https://researchseminars.org/talk/algebraic_geometry_FU/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Lai (Imperial College London)
DTSTART;VALUE=DATE-TIME:20210503T141500Z
DTEND;VALUE=DATE-TIME:20210503T154500Z
DTSTAMP;VALUE=DATE-TIME:20230208T081231Z
UID:algebraic_geometry_FU/3
DESCRIPTION:Title: Compactified Mirror Families for Log Calabi-Yau Surfaces
\nby Jonathan Lai (Imperial College London) as part of Algebraic geometry
Freie Universität Berlin\n\n\nAbstract\nWe present a compactification of
mirror families for positive pairs (Y\,D) where Y is a smooth projective s
urface and D is an anti-canonical cycle of rational curves. It ends up tha
t this compactified family can be realized as the moduli space of certain
marked pairs deformation equivalent to the original pair (Y\,D). To obtain
this identification\, the period associated to each fiber is computed usi
ng techniques from tropical geometry. This is ongoing joint work with Yan
Zhou.\n
LOCATION:https://researchseminars.org/talk/algebraic_geometry_FU/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lara Bossinger (UNAM Oaxaca)
DTSTART;VALUE=DATE-TIME:20210517T141500Z
DTEND;VALUE=DATE-TIME:20210517T154500Z
DTSTAMP;VALUE=DATE-TIME:20230208T081231Z
UID:algebraic_geometry_FU/4
DESCRIPTION:Title: Toric Degenerations: Embeddings and Projections\nby Lara
Bossinger (UNAM Oaxaca) as part of Algebraic geometry Freie Universität
Berlin\n\n\nAbstract\nI will report on joint work in progress with Takuya
Murata. We study toric degenerations\, i.e. flat families over the affine
line whose special fibre is a projective toric variety. They can be given
abstractly\, with an embedding or even have the property that there is a p
rojection from the generic to the special fiber. Algebraically the latter
corresponds to an embedding of the toric algebra into the homogeneous coor
dinate ring of the generic fibre. Using valuations and Gröbner theory to
give equations for embedded toric degenerations\, standard monomial theory
provides a useful tool to construct such projections.\n
LOCATION:https://researchseminars.org/talk/algebraic_geometry_FU/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marian Aprodu (University of Bucharest)
DTSTART;VALUE=DATE-TIME:20210531T141500Z
DTEND;VALUE=DATE-TIME:20210531T154500Z
DTSTAMP;VALUE=DATE-TIME:20230208T081231Z
UID:algebraic_geometry_FU/5
DESCRIPTION:Title: Green's conjecture and vanishing of Koszul modules\nby M
arian Aprodu (University of Bucharest) as part of Algebraic geometry Freie
Universität Berlin\n\n\nAbstract\nI report on a joint work with G. Farka
s\, S. Papadima\, C. Raicu and J. Weyman. Koszul modules are multi-linear
algebra objects associated to an arbitrary subspace in a second exterior p
ower. They are naturally presented as graded pieces of some Tor-s over the
dual exterior algebra. Koszul modules appear in Geometric Group Theory\,
in relations with Alexander invariants of groups. We prove an optimal vani
shing result for the Koszul modules\, and we use representation theory to
connect the syzygies of rational cuspidal curves to some particular Koszul
modules. We apply our vanishing result to Algebraic Geometry exhibiting a
new proof of Green’s conjecture on syzygies of canonical general curves
\, and to Geometric Group Theory.\n
LOCATION:https://researchseminars.org/talk/algebraic_geometry_FU/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Milena Wrobel (Universität Oldenburg)
DTSTART;VALUE=DATE-TIME:20210426T141500Z
DTEND;VALUE=DATE-TIME:20210426T154500Z
DTSTAMP;VALUE=DATE-TIME:20230208T081231Z
UID:algebraic_geometry_FU/6
DESCRIPTION:Title: Intrinsic Grassmannians\nby Milena Wrobel (Universität
Oldenburg) as part of Algebraic geometry Freie Universität Berlin\n\n\nAb
stract\nGeneralizing the well-known weighted Grassmanians introduced by Co
rti and Reid\, we introduce the notion of intrinsic Grassmannians\, i.e. n
ormal projective varieties whose Cox ring is defined by the Plücker ideal
$I_{k\,n}$. For $k = 2$\, we classify the smooth Fano ones having Picard
number two and give a concrete formula to compute their number for arbitra
ry $n$.\n
LOCATION:https://researchseminars.org/talk/algebraic_geometry_FU/6/
END:VEVENT
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SUMMARY:Aniket Shah (Ohio State University)
DTSTART;VALUE=DATE-TIME:20210614T141500Z
DTEND;VALUE=DATE-TIME:20210614T154500Z
DTSTAMP;VALUE=DATE-TIME:20230208T081231Z
UID:algebraic_geometry_FU/7
DESCRIPTION:Title: A q-analogue of Brion's identity from quasimap spaces\nb
y Aniket Shah (Ohio State University) as part of Algebraic geometry Freie
Universität Berlin\n\n\nAbstract\nFor a polytope P\, Brion's identity is
a useful formula for the lattice point generating function of P\, which wa
s originally proved via equivariant K-theory on the associated toric varie
ty X.\n\nWe prove a q-analogue of this identity via equivariant K-theory o
n certain compactifications of the space of maps from P^1 to X called quas
imap spaces\, which were introduced by Givental in the context of Gromov-W
itten theory. In the special case of P a standard simplex\, we obtain an i
dentity for the multivariate Rogers-Szego orthogonal polynomials as a sum
involving specializations of the quantum K-theoretic J-function.\n
LOCATION:https://researchseminars.org/talk/algebraic_geometry_FU/7/
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SUMMARY:Enrica Mazzon (MPI Bonn)
DTSTART;VALUE=DATE-TIME:20210607T141500Z
DTEND;VALUE=DATE-TIME:20210607T154500Z
DTSTAMP;VALUE=DATE-TIME:20230208T081231Z
UID:algebraic_geometry_FU/8
DESCRIPTION:Title: Toric geometry and integral affine structures in non-archime
dean mirror symmetry\nby Enrica Mazzon (MPI Bonn) as part of Algebraic
geometry Freie Universität Berlin\n\n\nAbstract\nThe SYZ conjecture is a
conjectural geometric explanation of mirror symmetry. Based on this\, Kon
tsevich and Soibelman proposed a non-archimedean approach to mirror symmet
ry. This led to the notion of essential skeleton and the construction of n
on-archimedean SYZ fibrations by Nicaise-Xu-Yu.\n\nIn this talk\, I will i
ntroduce these objects and report on recent results extending the approach
of Nicaise-Xu-Yu. This yields new types of non-archimedean retractions. F
or families of quartic K3 surfaces and quintic 3-folds\, the new retractio
ns relate nicely with the results on the dual complex of toric degeneratio
ns and on the Gromov-Hausdorff limit of the family.\n\nThis is based on a
work in progress with Léonard Pille-Schneider.\n
LOCATION:https://researchseminars.org/talk/algebraic_geometry_FU/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Krämer (Humboldt-Universität zu Berlin)
DTSTART;VALUE=DATE-TIME:20210628T141500Z
DTEND;VALUE=DATE-TIME:20210628T154500Z
DTSTAMP;VALUE=DATE-TIME:20230208T081231Z
UID:algebraic_geometry_FU/9
DESCRIPTION:Title: Big monodromy theorems on abelian varieties\nby Thomas K
rämer (Humboldt-Universität zu Berlin) as part of Algebraic geometry Fre
ie Universität Berlin\n\n\nAbstract\nLawrence and Sawin have shown that u
p to translation\, any abelian variety over a number field contains at mos
t finitely many smooth ample hypersurfaces with given class in the Néron-
Severi group and with good reduction outside a given finite set of primes.
A key ingredient in their proof is a big monodromy theorem for hypersurfa
ces\, which amounts to a statement about the Tannaka group of certain D-mo
dules on abelian varieties. In the talk I will give a motivated introducti
on to the geometry of such Tannaka groups and discuss recent progress towa
rds big monodromy theorems for subvarieties of higher codimension (this is
ongoing work with Ariyan Javanpeykar\, Christian Lehn and Marco Maculan).
\n
LOCATION:https://researchseminars.org/talk/algebraic_geometry_FU/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rita Pardini (University of Pisa)
DTSTART;VALUE=DATE-TIME:20210705T134500Z
DTEND;VALUE=DATE-TIME:20210705T144500Z
DTSTAMP;VALUE=DATE-TIME:20230208T081231Z
UID:algebraic_geometry_FU/10
DESCRIPTION:Title: Deformations of semi-smooth varieties\nby Rita Pardini
(University of Pisa) as part of Algebraic geometry Freie Universität Berl
in\n\n\nAbstract\nA variety X is semi-smooth if locally in the e'tale topo
logy its singularities are either double crossing points (xy=0) or pinch p
oints (x^2-y^2z=0). Alternatively\, X is semi-smooth if it can be obtained
from a smooth variety X' by gluing it along a smooth divisor D' via an in
volution g of D'. We describe explicitly in terms of the triple (X'\,D'\,
g) the two sheaves on X that control its deformation theory\, that is\, th
e tangent sheaf T_X and the sheaf T^1_X:=ext^1(\\Omega_X\,O_X). As an appl
ication\, we show the smoothability of the semi-smooth Godeaux surfaces (
K^2=1\, p_g=q=0).\nThis is joint work with Barbara Fantechi and Marco Fran
ciosi.\n\nPlease note the unusual time! This talk starts at 15:45 (Germany
/France/Italy times) on Monday the 5th of July.\n
LOCATION:https://researchseminars.org/talk/algebraic_geometry_FU/10/
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BEGIN:VEVENT
SUMMARY:Matteo Varbaro (University of Genova)
DTSTART;VALUE=DATE-TIME:20210621T141500Z
DTEND;VALUE=DATE-TIME:20210621T154500Z
DTSTAMP;VALUE=DATE-TIME:20230208T081231Z
UID:algebraic_geometry_FU/11
DESCRIPTION:Title: Singularities\, Serre conditions and h-vectors\nby Matt
eo Varbaro (University of Genova) as part of Algebraic geometry Freie Univ
ersität Berlin\n\n\nAbstract\nLet R be a standard graded algebra over a f
ield\, and denote by H_R(t) its Hilbert series. As it turns out\, multiply
ing H_R(t) by (1-t)^{dim R} yields a polynomial h((t)=h_0+h_1t+h_2t^2+…+
h_st^s\, known as the h-polynomial of R. It is well known and easy to prov
e that if R is Cohen-Macaulay h_i is nonnegative for all i.\nSince being C
ohen-Macaulay is equivalent to satisfying Serre condition (S_i) for all i\
, it is licit to ask if h_i is nonnegative for all i<=r whenever R satisfi
es (S_r).\nAs it turns out\, this is false in general\, but true putting s
ome additional assumptions on the singularities of R. In characteristic 0\
, it is enough that X= Proj R is Du Bois (in particular\, if X is smooth w
e have the desired nonnegativity). In positive characteristic\, assuming R
is F-split (equivalently\, if X=Proj R globally F-split)\, things work we
ll. In this talk I will speak of the above results and some of their conse
quences. This is a joint work with Hailong Dao and Linquan Ma.\n
LOCATION:https://researchseminars.org/talk/algebraic_geometry_FU/11/
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