Workshop on Algebraic Geometry

Time: Nov 2-3, 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
9:30-10:30	Rong Du	Uniform Vector Bundles on Rational Homogeneous spaces
10:50-11:50	Xin Lv	The irregularity of trigonal fibrations
12:00-13:30	Lunch
13:30-14:30	Hao Sun	Stability conditions and Fujita's conjecture
14:50-15:50	Zhan Li	Boundedness of the base varieties of certain fibrations
16:10-17:10	Feng Shao	The bigness of tangent bundles and cohomology of the twisted symmetric products of tangent bundles of irreducible Hermitian symmetric spaces
17:30-20:00	Dinner
November 03, 2020
9:30-10:30	Tong Zhang	Noether-Severi inequality and equality for irregular threefolds of general type
10:50-11:50	Xun Yu	Rational cubic fourfolds in Hassett divisors
12:00-13:30	Lunch
13:30-14:30	Yongqiang Liu	A question of Bobadilla-Kollár for the abelian variety case
14:50-15:50	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 semi-simple 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 Bobadilla-Kollár 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 non-trivial 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 by-product, 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 Noether-Lefschetz divisor of special cubic fourfolds contains a union of three codimension-two 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)

Noether-Severi inequality and equality for irregular threefolds of general type

In this talk, I will introduce the optimal Noether-Severi 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 Noether-Severi 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.