Algebraic Geometry Seminar
Philip Engel
UIC
Matroids and the integral Hodge conjecture for abelian varieties
Abstract: We will discuss a proof that the integral Hodge conjecture is false
for a very general abelian variety of dimension ≥ 4. Associated to
any regular matroid is a degeneration of principally polarized abelian
varieties. We introduce a new combinatorial invariant of regular
matroids, which obstructs the algebraicity of the minimal curve class,
on the very general fiber of the associated degeneration. In concert
with a result of Voisin, one deduces (via the intermediate Jacobian)
the stable irrationality of a very general cubic threefold. This is
joint work with Olivier de Gaay Fortman, and Stefan Schreieder.
Monday September 22, 2025 at 3:00 PM in 636 SEO