Algebraic
Geometry in East Asia
Online Seminar
This
is a joint effort of many algebraic geometers in East Asia. We aim to create a
platform for algebraic geometers and students for further interaction and
cooperation.
The
seminar will take place on Friday at GMT 1:00 or GMT 7:00, unless otherwise
specified, in order to accommodate most participants in East Asia.
To
receive the announcement and the Zoom password, please send an empty mail with
the title "Subscription" to the following address:
ageaseminar A@T gmail.com
This is a mirror site of
https://sites.google.com/ncts.ntu.edu.tw/ageaseminar
Last updated 2021/02/18
Upcoming Talks:
2021/03/05 GMT 7:008:00
Junyi Xie (CNRS Rennes)
Title: Some boundedness problems in Cremona
group
Abstract: This talk is based on a work
with Cantat and Deserti. According
to the degree sequence, there are 4 types (elliptic, Jonquieres,
Halphen and Loxodromic) of elements f in
Bir(P^2). For a fixed degree d>=1, we study the set of these 4 types
of elements of degree d. We show that for Halphen
twists and Loxodromic transformations, such sets are constructible. This
statement is not true for elliptic and Jonquieres elements.We also show that for a Jonquieres or Halphen twist f of
degree d, the degree of the unique finvariant pencil is bounded by a constant
depending on d. This result may be considered as a positive answer to the
Poincare problem of bounding the degree of first integrals,but for birational twists instead of
algebraic foliations. As a consequence of this, we show that for two Halphen twists f and g, if they are conjugate in Bir(f),
then they are conjugate by some element of degree bounded by a constant
depending on deg(f)+deg(g). This statement is not true for Jonquieres
twists.
2021/03/05 GMT 8:159:15
Guolei Zhong(National
University of Singapore)
Title: Fano threefolds
and fourfolds admitting nonisomorphic endomorphisms.
Abstract: In this talk, we first show that
a smooth Fano threefold X admits a nonisomorphic surjective endomorphism if
and only if X is either toric or a product of a
smooth rational curve and a del Pezzo surface.
Second, we show that a smooth Fano fourfold Y with a conic bundle structure is toric if and only if Y admits an amplified endomorphism. The
first part is a joint work with Sheng Meng and DeQi Zhang, and the second part
is a joint work with Jia jia.
Date 
Time 
Speaker 
Title 
2021/03/05 
GMT
7 
Junyi Xie (CNRS Rennes) 
Some boundedness problems in Cremona group 
2021/03/05 
GMT
8:15 
Guolei Zhong(National University of Singapore) 
Fano threefolds and
fourfolds admitting nonisomorphic endomorphisms 
2021/03/19 
GMT
1 
Zhiyuan Li (Shanghai Center for Mathematical Sciences) 

2021/03/19 
GMT
2:15 
Michael Kemeny
(University of WisconsinMadison) 

2021/04/02 
GMT
7 
Weizhe Zheng (Morningside Center of Mathematics) 

2021/04/02 
GMT
8:15 
Kestutis Cesnavicius (Paris Sud) 

2021/04/16 
GMT
1 
KuanWen Lai (University of Massachusetts Amherst) 

2021/04/16 
GMT
2:15 
YuShen Lin (Boston University) 

2021/04/30 
GMT
7 
Yi Gu (Suzhou University) 

2021/04/30 
GMT
8:15 
Takehiko Yasuda (Osaka University) 

2021/05/14 
GMT
7 
Yuji Odaka (Kyoto
University) 





More Confirmed Speakers:
Organizers: Yujiro Kawamata
(Tokyo), Xiaotao Sun (Tianjin), JongHae
Keum (KIAS, Seoul), Jungkai Chen (NTU, Taipei), Conan
Nai Chung Leung (CUHK, Hong Kong), Phung Ho Hai
(VAST, Hanoi), De Qi Zhang (NUS, Singapore), Yusuke Nakamura (Tokyo), Baohua Fu (CAS, Beijing), Kiryong
Chung (Kyungpook National Univ., Daegu), HsuehYung Lin (IPMU, Tokyo)
Archive:
2020/08/07 GMT 8:009:00
Caucher Birkar (University of Cambridge)
Title:
Geometry and moduli of polarised varieties
Abstract:
In this talk I will discuss
projective varieties polarised by ample divisors (or
more generally nef and big divisors) and outline some
recent results about the geometry and moduli spaces of such varieties.
2020/08/14
GMT 7:008:00
Yukinobu
Toda (Kavli IPMU) (video)
Title: On
dcritical birational geometry and categorical DT theories
Abstract:
In this talk, I will explain an
idea of dcritical birational geometry, which deals with certain
"virtual" birational maps among schemes with dcritical structures.
One of the motivations of this new framework is to categorify wallcrossing
formulas of DonaldsonThomas invariants. I will propose an analogue of D/K
equivalence conjecture in dcritical birational geometry, which should lead to
a categorification of wallcrossing formulas of DT invariants.
The main result in this talk is
to realize the above story for local surfaces. I will show the window theorem
for categorical DT theories on local surfaces, which is used to categorify
wallcrossing invariance of genus zero GV invariants, MNOP/PT correspondence,
etc.
2020/08/14
GMT 8:159:15
HuaiLiang
Chang (HKUST) (video)
Title:
BCOV Feynman structure for Gromov Witten invariants
Abstract:
Gromov
Witten invariants Fg encodes the numbers of genus g
curves in Calabi Yau threefolds. They play a role in enumerative geometry and
are not easy to be determined.
In 1993 Bershadsky,
Cecotti, Ooguri, Vafa exhibited a hidden "Feynman structure"
governing all Fg’s at once. Their argument was via
path integral while its counterpart in mathematics had been missing for
decades.
In 2018, considering the moduli
of a special kind of algebro geometric objects,
"Mixed Spin P fields", is developed and provides the wanted
"Feynman structure". In this talk we will see genuine ideas behind
these features.
2020/08/28 GMT 7:008:00
Xun Yu
(Tianjin University) (video)
Title: Automorphism groups of smooth
hypersurfaces
Abstract:
I
will discuss automorphism groups of smooth hypersurfaces in the projective
space and explain an approach to classify automorphism groups of smooth quintic threefolds and smooth
cubic threefolds. This talk is based on my joint
works with Professor Keiji Oguiso
and Li Wei.
2020/08/28 GMT
8:159:15
Tuyen Trung Truong
(University of Oslo) (video)
Title: Rationality of quotients of
Abelian varieties and computer algebra
Abstract:
This
talk concerns the question of what variety of the form X/G, where X is an
Abelian variety and G a finite subgroup of Aut(X), is
rational. It is motivated by some interesting geometric and dynamical system
questions. Most of the work so far concerns the case where X is of the form E^m where E is an elliptic curve, and G is a finite
subgroup of Aut(E). I will review the current known
results and approaches, and explain why it could be necessary to use computer
algebra to resolve the question, and a brief discussion on works in this
direction (including my ongoing joint work with Keiji
Oguiso).
2020/09/11 GMT 2:153:15
Jeongseok Oh (KIAS) (video)
Title: Counting sheaves on CalabiYau 4folds
Abstract:
We define a localised Euler class for
isotropic sections, and isotropic cones, in SO(N) bundles. We use this to give
an algebraic definition of BorisovJoyce sheaf counting invariants on CalabiYau 4folds. When a torus acts, we prove a localisation result. This talk is based on the joint work
with Richard. P. Thomas.
2020/09/25 GMT 7:008:00
Jie Liu
(Chinese Academy of Sciences) (video)
Title:
Strictly nef subsheaves in tangent bundle
Abstract:
Since the seminal works of Mori
and SiuYau on the solutions to Hartshorne conjecture
and Frankel conjecture, it becomes apparent that the positivity of the tangent
bundle of a complex projective manifold carries important geometric
information. In this talk, we will discuss the structure of projective
manifolds whose tangent bundle contains a locally free strictly nef subsheaf and present a new characterisation
of projective spaces. This is a joint work with Wenhao
Ou (AMSS) and Xiaokui Yang
(YMSC).
2020/09/25 GMT 8:309:30
Junyan Cao (Université Côte d'Azur) (video)
Title: On
the OhsawaTakegoshi extension theorem
Abstract:
Since it was established, the OhsawaTakegoshi extension theorem turned out to be a
fundamental tool in complex geometry. We establish a new extension result for
twisted canonical forms defined on a hypersurface with simple normal crossings
of a projective manifold with a control on its L^{2} norme. It is a joint work with Mihai Păun.
2020/10/9 GMT 7:008:00
Frank Gounelas (Göttingen
University) (video)
Title: Curves
on K3 surfaces
Abstract:
I will survey the recent completion (joint with ChenLiedtke)
of the remaining cases of the conjecture that a projective K3 surface contains
infinitely many rational curves. As a consequence of this along with the BogomolovMiyaokaYau inequality and the deformation theory
of stable maps, I will explain (joint with Chen) how in characteristic zero one
can deduce the existence of infinitely many curves of any geometric genus
moving with maximal variation in moduli on a K3 surface. In particular this
leads to an algebraic proof of a theorem of Kobayashi on vanishing of global
symmetric differentials and applications to 0cycles.
2020/10/9
GMT 8:159:15
Toshiyuki Katsura (University of Tokyo) (video)
Title: Counting Richelot
isogenies of superspecial curves of genus 2
Abstract:
Recently,
supersingular elliptic curve isogeny cryptography has
been extended to the genus2 case by using superspecial
curves of genus 2 and their Richelot isogeny graphs.
In view of this situation, we examine the structure of Richelot
isogenies of superspecial curves of genus 2, and give
a characterization of decomposed Richelot isogenies.
We also give a concrete formula of the number of such decomposed Richelot isogenies up to isomorphism between superspecial principally polarized abelian surfaces. This
is a joint work with Katsuyuki Takashima (Mitsubishi Electic Co.).
2020/10/23 GMT 7:008:00
Takahiro Shibata (National
University of Singapore) (video)
Title: Invariant subvarieties
with small dynamical degree
Abstract:
Given a selfmorphism on an algebraic
variety, we can consider various dynamical problems on it. Motivated by an
arithmeticdynamical problem, we consider invariant subvarieties
whose first dynamical degree is less than that of the ambient variety. We give
an estimate of the number of them in certain cases.
2020/10/23 GMT 8:159:15
Sheng Meng (KIAS) (video)
Title: Dynamical equivariant minimal model program
Abstract:
I will describe the minimal model
program (MMP) in the study of complex dynamics and how MMP can be applied to
many conjectures with dynamical or arithmetical flavours.
Several open questions will also be proposed in this talk.
2020/11/06 GMT 1:002:00
Hong
Duc Nguyen
(Thang Long University) (video)
Title: Cohomology
of contact loci
Abstract:
We
construct a spectral sequence converging to the cohomology
with compact support of the $m$th contact locus of a
complex polynomial. The first page
is explicitly described in terms of a log resolution and coincides with the
first page of McLean's spectral sequence converging to the Floer
cohomology of the $m$th iterate
of the monodromy, when the polynomial has an isolated
singularity. Inspired by this connection we conjecture that the Floer cohomology of the $m$th iterate of the monodromy of
$f$ is isomorphic to the compactly supported cohomology
of the $m$th contact locus of $f$, and that this
isomorphism comes from an isomorphism of McLean spectral sequence with ours.
2020/11/06 GMT 1:002:00
Qizheng Yin (Peking University) (video)
Title:
The Chow
ring of Hilb(K3) revisited
Abstract:
The
Chow ring of hyperKähler varieties should enjoy
similar properties as the Chow ring of abelian varieties. In particular, a Beauville type decomposition is believed (by Beauville himself) to exist for all hyperKähler varieties. In this talk, we discuss a general
approach towards the Beauville type decomposition of
the Chow ring. We carry it out explicitly for the Hilbert scheme of points of
K3 surfaces, and prove the multiplicativity of the resulting decomposition.
Joint work with Andrei Negut and Georg Oberdieck.
2020/11/20 GMT 7:008:00
Jinhyung Park (Sogang
University) (video)
Title: A CastelnuovoMumford
regularity bound for threefolds with mild
singularities
Abstract:
The
EisenbudGoto regularity conjecture says that the CastelnuovoMumford regularity of an embedded projective
variety is bounded above by degree  codimension +1, but McCulloughPeeva recently constructed highly singular counterexamples
to the conjecture. It is natural to make a precise distinction between mildly
singular varieties satisfying the regularity conjecture and highly singular
varieties not satisfying the regularity conjecture. In this talk, we consider
the threefold case. We prove that every projective threefold with rational
singularities has a nice regularity bound, which is slightly weaker than the
conjectured bound, and we show that every normal projective threefold with
CohenMacaulay Du Bois singularities in codimension
two satisfies the regularity conjecture. The codimension two case is
particularly interesting because one of the counterexamples to the regularity
conjecture appears in this case. This is joint work with Wenbo
Niu.
2020/11/20 GMT 7:008:00
Evgeny Shinder (University of Sheffield) (video)
Title: Semiorthogonal decompositions
for singular varieties
Abstract:
I
will explain a semiorthogonal decomposition for derived categories of singular projective
varieties into derived categories of finitedimensional algebras, due to
Professor Kawamata, generalizing the concept of an
exceptional collection in the smooth case. I will present known constructions
of these for nodal curves (Burban), torsionfree toric surfaces (KarmazynKuznetsovShinder) and two nodal threefolds
(Kawamata). Finally, I will explain obstructions
coming from the K_{1} group, and how it translates to
maximal nonfactoriality in the nodal threefold case.
This is joint work with M. Kalck and N. Pavic.
2020/12/4 GMT
1:002:00
Jakub Witaszek (University of Michigan) (video)
Title: On the fourdimensional Minimal Model
Program for singularities and families in positive characteristic
Abstract:
I will discuss new developments on the fourdimensional
Minimal Model Program in positive characteristic. This is based on a joint work
with Christopher Hacon.
2020/12/4 GMT
2:153:15
YuWei Fan (UC Berkeley) (video)
Title: Stokes matrices, surfaces, and points
on spheres
Abstract:
Moduli spaces of points on nspheres carry natural
actions of braid groups. For n=0,1, and 3, we prove that these symmetries
extend to actions of mapping class groups of positive genus surfaces, through
exceptional isomorphisms with certain moduli of local systems. This relies on
the existence of group structure for spheres in these dimensions. We also apply
the exceptional isomorphisms to the study of Stokes matrices and exceptional
collections of triangulated categories. Joint work with Junho
Peter Whang.
2020/12/18 GMT
7:008:00
Chen Jiang (Fudan University) (video)
Title: Positivity in hyperk\"{a}hler manifolds via RozanskyWitten
theory
Abstract:
For a hyperk\"{a}hler manifold $X$ of dimension $2n$, Huybrechts
showed that there are constants $a_0, a_2, \dots, a_{2n}$
such that
$$\chi(L) =\sum_{i=0}^n\frac{a_{2i}}{(2i)!}q_X(c_1(L))^{i}$$
for any line bundle $L$ on $X$, where $q_X$ is the BeauvilleBogomolovFujiki
quadratic form of $X$. Here the polynomial
$\sum_{i=0}^n\frac{a_{2i}}{(2i)!}q^{i}$ is called the RiemannRoch polynomial
of $X$.
In this talk, I will discuss recent progress on the
positivity of coefficients of the RiemannRoch polynomial
and also positivity of Todd classes. Such positivity results follows
from a Lefschetztype decomposition of the root of Todd
genus via the Rozansky—Witten theory, following the
ideas of Hitchin, Sawon, and
NieperWißkirchen.
2020/12/18 GMT
8:159:15
Ya Deng (IHES) (video)
Title: Big Picard theorem for varieties
admitting a variation of Hodge structures
Abstract:
In 1972, A. Borel proved
generalized big Picard theorem for any hermitian locally
symmetric variety $X$: any holomorphic map from the punctured disk to $X$ extends
to a holomorphic map of the disk into any projective compactification of $X$.
In particular any analytic map from a quasiprojective variety to $X$ is
algebraic. Period domains, introduced by Griffiths in 1969, are classifying spaces
for Hodge structures. They are transcendental generalizations of hermitian locally symmetric varieties. In this talk, I will
present a generalized big Picard theorem for period domains, which extends the recent
work by BakkerBrunebarbeTsimerman.
2021/1/8 GMT 1:002:00
Junliang Shen (MIT) (video)
Title: Intersection cohomology
of the moduli of of 1dimensional sheaves and the
moduli of Higgs bundles
Abstract:
In general, the topology of the moduli space of semistable sheaves on an algebraic variety relies heavily
on the choice of the Euler characteristic of the sheaves. We show a striking
phenomenon that, for the moduli of 1dimensional semistable
sheaves on a toric del Pezzo
surface (e.g. P^2) or the moduli of semistable Higgs
bundles with respect to a divisor of degree > 2g2 on a curve, the
intersection cohomology (together with the perverse
and the Hodge filtrations) of the moduli space is independent of the choice of
the Euler characteristic. This confirms a conjecture of Bousseau
for P^2, and proves a conjecture of Toda in the case of certain local CalabiYau 3folds. In the proof, a generalized version of Ngô's support theorem plays a crucial role. Based on joint
with Davesh Maulik.
2021/1/8 GMT
2:153:15
Yohsuke Matsuzawa (Brown University) (video)
Title: Vojta's conjecture
and arithmetic dynamics
Abstract:
I will discuss applications of Vojta's
conjecture to some problems in arithmetic dynamics, concerning the growth of
sizes of coordinates of orbits, greatest common divisors among coordinates, and
prime factors of coordinates. These problems can be restated and generalized in
terms of (local/global) height functions, and I proved estimates on asymptotic
behavior of height functions along orbits assuming Vojta's
conjecture. One of the key inputs is an asymptotic estimate of log canonical
thresholds of (X, f^{n}(Y)), where f : X>X is a
selfmorphism and Y is a closed subscheme of X.
As corollaries, I showed that Vojta's conjecture implies Dynamical LangSiegel conjecture
for projective spaces (the sizes of coordinates grow in the same speed),and existence of primitive prime divisors in higher
dimensional setting.
2021/1/22 GMT
7:008:00
Sho Tanimoto (Kumamoto University)
Title: Classifying sections of del Pezzo fibrations
Abstract:
Mori invented a technique called as Bend and Break lemma which
claims that if we deform a curve with fixed points, then it breaks into the
union of several curves such that some of them are rational. This technique has
wide applications ranging from rationally connectedness of smooth Fano varieties,
Cone theorem for smooth projective varieties, to boundedness of smooth Fano
varieties. However, a priori there is no control on breaking curves so in
particular, an outcome of Bend and Break could be a singular point of the moduli
space of rational curves. With Brian Lehmann, we propose Movable Bend and Break
conjecture which claims that a free rational curve of enough high degree can
degenerate to the union of two free rational curves in the moduli space of
stable maps, and we confirm this conjecture for sections of del Pezzo fibrations over an arbitrary
smooth projective curve. In this talk I will explain some of ideas of the proof
of MBB for del Pezzo fibrations
as well as its applications to Batyrev’s conjecture and
Geometric Mann’s conjecture. This is joint work with Brian Lehmann.
2021/1/22 GMT
8:159:15
Fei Hu (University of Oslo)
Title: Some comparison problems on correspondences
Abstract:
Although the transcendental part of Weil's
cohomology theory remains mysterious, one may try to
understand it by investigating the pullback actions of morphisms, or more generally,
correspondences, on the cohomology group and its
algebraic part.
Inspired by a result of Esnault and Srinivas on automorphisms of surfaces as well as
recent advances in complex dynamics, Truong raised a question on the comparison
of two dynamical degrees, which are defined using pullback actions of dynamical
correspondences on cycle class groups and cohomology groups,
respectively. An affirmative answer to his question would surprisingly imply
Weil’s Riemann hypothesis.
In this talk, I propose more general comparison
problems on the norms and spectral radii of the pullback actions of certain
correspondences (which are more natural in some sense). I will talk about their
connections with Truong’s dynamical degree comparison and the standard
conjectures. Under certain technical assumption, some partial results will be
given. I will also discuss some applications to Abelian varieties and surfaces.
This talk is based on joint work with Tuyen Truong.
2021/2/5 GMT 1:002:00
Lei Zhang (USTC)
Title: Counterexample to Fujita conjecture in
positive characteristic
Abstract:
Fujita conjecture was proposed over complex
numbers, which predicts that for a smooth projective variety X and an ample
line bundle L on X, K_X + (dim X+1)L is base point
free and K_X + nL is very ample if n > dim X+1.
Joint with Yi Gu, Yongming Zhang, we find counterexamples to this elegant conjecture
in positive characteristic. These examples stem from Raynaud’s surfaces. I will
first report some related results on this topic and explain the construction
and the proof.
2021/02/19 GMT 7:008:00
Joonyeong Won (KIAS)
Title: SasakiEinstein and KählerEinstein metric on 5manifolds and weighted hypersurfaces
Abstract: By developing the method introduced by
Kobayashi in 1960's, Boyer, Galicki and Kollár found many examples of simply connected Sasaki Einstein
5manifolds. For such examples they verified existence of orbifold KählerEinstein metrics on various log del Pezzo surfaces, in particular weighted log del Pezzo hypersurfaces. We discuss about recent progresses of the
existence problem of Sasaki Einstein and KählerEinstein
metric on 5manifold and weighted del Pezzo hypersurfaces
respectively.
2021/02/19 GMT 8:159:15
Soheyla Feyzbakhsh (Imperial College)
Title: An application of a BogomolovGieseker type inequality to counting invariants
Abstract: In this talk, I will work on a smooth
projective threefold X which satisfies the BogomolovGieseker
conjecture of BayerMacr\`iToda,
such as the projective space P^3 or the quintic threefold.
I will show certain moduli spaces of 2dimensional torsion sheaves on X are
smooth bundles over Hilbert schemes of ideal sheaves of curves and points in X.
When X is CalabiYau this gives a simple wall crossing
formula expressing curve counts (and so ultimately GromovWitten
invariants) in terms of counts of D4D2D0 branes. This is joint work with
Richard Thomas.
Sponsors: National Center for Theoretical Sciences