Events

The perverse filtration captures interesting homological information of algebraic maps. Recent studies of integrable systems (e.g. Hitchin systems, Beauville-Mukai systems) suggest 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 both 1) and 2) for a natural class of abelian fibrations, namely fibrations in compactified Jacobians. I will discuss several ingredients from (coherent) derived categories, K-theory/Chow theory, and constructible categories, as well as some applications of our result. Joint work in progress with Davesh Maulik and Junliang Shen.