Algebraic Geometry Seminar: Cohomology and cycles on compactified Jacobians, by Younghan Bae
February 23, 2026
3:00 PM - 3:50 PM
Younghan Bae (University of Michigan): Cohomology and cycles on compactified Jacobians
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.
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Date posted
Mar 5, 2026
Date updated
Mar 5, 2026
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