The perverse filtration of abelian fibrations via Fourier-Mukai

Abstract

The perverse (Leray) filtration captures key topological information of algebraic maps. Recent studies of integrable systems (e.g. Hitchin system, Beauville-Mukai system) suggests two common features of the perverse filtration of abelian fibrations:

1) the perverse filtration is multiplicative with respect to the cup product;

2) the perversity of tautological classes is governed by the Chern degree.

In this talk, I will explain a unified approach to the two statements above for a large class of abelian fibrations, namely fibrations in compactified Jacobians. It uses a combination of Arinkin’s Fourier-Mukai theory, Ngô’s support theorem, and Chow-theoretic/motivic techniques. I will also discuss some applications to earlier work of Maulik-Yun and to the P = W conjecture of de Cataldo-Hausel-Migliorini. Joint work in progress with Davesh Maulik and Junliang Shen.

About the speaker

訚琪峥，2013年博士毕业于法国巴黎第六大学和荷兰奈梅亨大学数学系，曾在瑞士苏黎世联邦理工学院做博士后研究。他于2017年加入北京国际数学研究中心，主要研究领域是代数几何。