北京代数几何日

BEIJING ALGEBRAIC GEOMETRY DAY

2025年8月23日 @清华大学，双清综合楼B725

报名日期：2025年8月1日-16日

报名链接：https://www.wjx.cn/vm/QFRWhmw.aspx#

报告人

邓亚（CNRS, Université de Lorraine）

胡佳俊（清华大学）

江孝炜（清华大学）

王博潼（University of Wisconsin-Madison）

夏铭辰（中国科学技术大学）

日程安排   

报告题目与摘要

报告人：邓亚

题目：Deformation of Algebraic Varieties with Big Fundamental Groups

摘要：In 2002, De Oliveira, Katzarkov, and Ramachandran conjectured that the property of having a big fundamental group should be preserved under small smooth deformations of complex projective varieties--an analogue of Siu’s invariance of plurigenera. Until recently, this conjecture was only proved for surfaces and, under additional assumptions, for certain threefolds by Benoît Claudon in his PhD thesis in 2007. In this talk I will explain our recent proof of this conjecture in the case where the fundamental group is linear, i.e., admits an almost faithful linear representation. I will outline the main ideas of the proof, which combine non-abelian Hodge theory with new techniques involving the deformation of harmonic maps to Euclidean buildings. I will also give an application to the deformation openness of pseudo-Brody hyperbolicity. This is based on a joint work with Chikako Mese and Botong Wang.

报告人：江孝炜

题目：Boundedness of Polarized Log Calabi–Yau Fibrations with Bounded Bases

摘要：In this talk, we discuss the boundedness problem for log Calabi–Yau fibrations whose bases and general fibers are bounded. We show that, after fixing certain natural invariants, the total spaces of such fibrations are bounded in codimension one. Furthermore, we prove that the total spaces themselves are bounded when the general fibers have vanishing irregularity. As an application, we obtain boundedness results for stable minimal models and fibered Calabi–Yau varieties. This is based on joint work with Junpeng Jiao and Minzhe Zhu.

报告人：王博潼

题目：TBA

摘要：TBA

报告人：夏铭辰

题目：Transcendental b-divisors

摘要：I will explain the notion of b-divisors over a compact Kähler manifold. We will show that nef b-divisors, being a cohomological notion, are in bijection with a class of currents. The analytic theory can therefore be applied while studying nef b-divisors. As a consequence, we establish the intersection theory of nef b-divisors, answering a question of Dang-Favre.

报告人：胡佳俊

题目：The kernel of Lefschetz-type operators and extremals of geometric inequalities

摘要：Motivated by convex geometry and the Hodge-theoretic study of the topology of algebraic varieties, we investigate the kernel of Lefschetz-type operators arising from complete intersections of nef divisors. We provide a complete characterization for supercritical collections of n-2 semiample divisors, thereby resolving a conjecture of Shenfeld and van Handel. As applications, we characterize the extremals of the Khovanskii-Teissier inequalities in the case of two semiample divisors, and we give an algebro-geometric proof of the extremals of the Alexandrov-Fenchel inequalities for rational convex polytopes in the supercritical setting. This is joint work with Jian Xiao.