Younghan Bae : Cohomology and cycles on compactified Jacobians

Posted by Philip Engel , part of the Algebraic Geometry Seminar.

At

Feb. 23, 2026, 3 p.m.

In

636 SEO

Abstract

By Beauville, and Deninger-Murre, cycles on abelian schemes have a multiplicative weight decomposition. Recent developments surrounding the moduli space of Higgs bundles suggest that analogous properties may hold for abelian fibrations with singular fibers. In this talk, I will study the cohomological and Chow theoretic study of fine compactified Jacobians. I will first show that there exist two fine compactified Jacobians whose rational cohomology rings are not isomorphic. To address this issue, we degenerate the ring structure via the perverse filtration, and prove that the resulting ring is independent of the choice of stability condition. This intrinsic ring structure further lifts to the level of algebraic cycles. Finally I will present explicit calculations using the Fourier transform and logarithmic Abel-Jacobi theory. This is a joint work with D. Maulik, J. Shen, Q. Yin; A. Pixton; and S. Molcho and A. Pixton.