The Picard group of moduli spaces of K3 surfaces and their compactifications

• 主讲人：Zhiyuan Li (Shanghai Center for Mathematical Sciences, Fudan University)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2024-10-31 21:00 - 2024-10-31 22:00
• 地点： Online

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Recording: https://disk.pku.edu.cn/link/AABCAC4B4FB4294DCEAE32637CBB69A429

 

Abstract: The study of Picard group of moduli spaces is an important question in moduli theory. Since from Mumford's famous paper “Picard groups of moduli problems”, algebraic geometers have investigated the Picard group of moduli space of smooth curves and its compactifications. It has been shown by Harer and Arbarello-Cornalba that M_g has Picard number one while its Deligne-Mumford compactification \overline{M}_g has Picard number 2+[g/2]. In this talk, I will survey the recent progress for moduli spaces of projective K3 surfaces and their compactifications. We will give a complete description of their Picard groups. 

 

Bio: Zhiyuan Li is a dual-appointed professor at Shanghai Center for Mathematical Sciences and School of Mathematical Sciences of Fudan University. He was selected for the National High level Talent Program. He graduated from University of Science and Technology of China in 2004, and received the PhD degree from Rice University in 2012. He has worked as a postdoctoral fellow at Stanford University and University of Bonn.

Professor Zhiyuan Li is mainly engaged in the research of algebraic geometry and related fields and has made a series of achievements in moduli space in algebraic geometry and hyper-Kähler Geometry. He has solved long-term unsolved public problems such as the Noether-Lefschetz conjecture on the moduli space of K3 surfaces and the special Hodge conjecture on orthogonal Shimura varieties, and published a number of papers in important international journals such as Inventions and Duke Mathematical Journal.