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【2020.11.02-11.03 北京】Workshop on Algebraic Geometry
2020-10-30 | 编辑：

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 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)

# 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)

# 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)

# 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)

# 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)

Hao Sun ()

# 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)

# 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)

# 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)

# 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.

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