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            现在位置:首页 > 学术会议
        【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

        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 Hassetts 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.

         

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