On the Perversity of Chern Classes for Compactified Jacobians

TL;DR

This paper establishes bounds on the perversity of Chern classes for compactified Jacobian fibrations, providing motivic insights and a filtration version of a recent conjecture, advancing understanding of their geometric and algebraic properties.

Contribution

It introduces new perversity bounds for Chern classes of compactified Jacobians and proves a filtration version of a recent conjecture, with motivic methods.

Findings

Chern classes of compactified Jacobians have perversity ≤ k

Established a motivic framework for perversity bounds

Proved a filtration version of a recent conjecture

Abstract

We prove some perversity bounds for the Chern classes of a compactified Jacobian fibration, namely the $k$-th Chern class of the compactified Jacobian has perversity $\leq k$. Our results are motivic in nature, and we also prove a filtration version of a conjecture raised in arXiv:2402:08861.