Algebraic Geometry Seminar
Younghan Bae
University of Michigan
Cohomology and cycles on compactified Jacobians
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.
Monday February 23, 2026 at 3:00 PM in 636 SEO