Workshop on Algebraic Geometry
Time: Nov 23, 2020
Venue: N202, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Invited Speakers
Rong Du

East China Normal University

Zhan Li

Southern University of Science and Technology

Yongqiang Liu

University of Science and Technology of China

Xin Lv

East China Normal University

Feng Shao

Academy of Mathematics and System Sciences, CAS

Hao Sun

Shanghai Normal University

Xun Yu

Tianjin University

Tong Zhang

East China Normal University

Mingshuo Zhou

Tianjin University

Organizers
Yifei Chen

AMSS CAS

Baohua Fu

MCM AMSS

Jie Liu

AMSS CAS

Conference Schedule
November 02, 2020

9:3010:30

Rong Du

Uniform Vector Bundles on Rational Homogeneous spaces

10:5011:50

Xin Lv

The irregularity of trigonal fibrations

12:0013:30

Lunch

13:3014:30

Hao Sun

Stability conditions and Fujita's conjecture

14:5015:50

Zhan Li

Boundedness of the base varieties of certain fibrations

16:1017:10

Feng Shao

The bigness of tangent bundles and cohomology of the twisted symmetric products of tangent bundles of irreducible Hermitian symmetric spaces

17:3020:00

Dinner

November 03, 2020

9:3010:30

Tong Zhang

NoetherSeveri inequality and equality for irregular threefolds of general type

10:5011:50

Xun Yu

Rational cubic fourfolds in Hassett divisors

12:0013:30

Lunch

13:3014:30

Yongqiang Liu

A question of BobadillaKollár for the abelian variety case

14:5015:50

Mingshuo Zhou

Moduli space of parabolic bundles over a curve

Titles and Abstracts
Rong Du (East China Normal University)
Uniform Vector Bundles on Rational Homogeneous spaces
We will introduce the background of uniform vector bundles on special rational homogeneous spaces and the relation between rational homogeneous spaces and marked Dynkin diagrams of semisimple Lie algebras. Furthermore, we will talk about an open problem on classifying low rank uniform vector bundles on rational homogeneous spaces. This is a joint work with Xinyi Fang and Yun Gao.
Zhan Li (Southern University of Science and Technology)
Boundedness of the base varieties of certain fibrations
It is conjectured that the base varieties of the Iitaka fibrations are bounded when the Iitaka volumes are bounded above. We confirm this conjecture for Iitaka ？lc Fano type fibrations. When time permits, we will also discuss relevant problems in real coefficients.
Yongqiang Liu (University of Science and Technology of China)
A question of BobadillaKollár for the abelian variety case
In their 2012 paper, Bobadilla and Kollár studied topological conditions which guarantee that a proper map of complex algebraic varieties is a topological or differentiable fibration. They also asked whether a certain finiteness property on the relative covering space can imply that a proper map is a fibration. In this talk, we answer positively the integral homology version of their question in the case of abelian varieties. This is based on a joint work with Laurentiu Maxim and Botong Wang (arXiv:2006.09295).
Xin Lv (East China Normal University)
The irregularity of trigonal fibrations
Let $f: S \to B$ be a nontrivial fibration of curves of genus $g$. Xiao conjectured an upper bound of the relative irregularity $q_f$ in terms of the genus $g$. In this talk, we consider this problem for trigonal fibrations.
Feng Shao (Academy of Mathematics and System Sciences, CAS)
The bigness of tangent bundles and cohomology of the twisted symmetric products of tangent bundles of irreducible Hermitian symmetric spaces
Let $X$ be an irreducible Hermitian symmetric space of compact type embedded minimally into a projective space by a very ample line bundle $\mathcal{O}_X(1)$. In this paper, we give the irreducible decomposition of $Sym^r T_X$ and calculate the cohomology group $H^p(X,Sym^r T_X\otimes \mathcal{O}_X(d))$. As a byproduct, we give a cohomological characterization of the rank of $X$. Moreover, we define a number to characterize the bigness of the tangent bundle of smooth complex projective varieties and calculate this number for every irreducible Hermitian symmetric space of compact type.
Hao Sun (Shanghai Normal University)
Stability conditions and Fujita's conjecture
We will introduce the definition of Bridgeland stability conditions and its application to Fujita's conjecture for threefolds. This approach to Fujita's conjecture is a natural generalization of Reider's method.
Xun Yu (Tianjin University)
Rational cubic fourfolds in Hassett divisors
We prove that every Hassett’s NoetherLefschetz divisor of special cubic fourfolds contains a union of three codimensiontwo subvarieties, parametrizing rational cubic fourfolds, in the moduli space of smooth cubic fourfolds. This is a joint work with Song Yang.
Tong Zhang(East China Normal University)
NoetherSeveri inequality and equality for irregular threefolds of general type
In this talk, I will introduce the optimal NoetherSeveri inequality for complex irregular threefolds of general type. This answers an open question of Z. Jiang in dimension three. I will also talk about the complete classification of those irregular threefolds attaining the NoetherSeveri equality. This is a joint work with Y. Hu.
Mingshuo Zhou(Tianjin University)
Moduli space of parabolic bundles over a curve
In this talk, we will present some progress on moduli space of parabolic bundles over a curve. We will also introduce some questions in this topic. This is a joint work with Professor Xiaotao Sun.