Philip Engel : Matroids and the integral Hodge conjecture for abelian varieties

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

At

Sept. 22, 2025, 3 p.m.

In

636 SEO

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.