Workshop on Recent Developments in Hodge Theory and O-minimality
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.
Date & Time
March 09, 2026 | 2:30pm – 3:30pm
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03/09/2026 14:30
03/09/2026 15:30
Workshop on Recent Developments in Hodge Theory and O-minimality
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Topic: Matroids and the Integral Hodge Conjecture for Abelian Varieties
Speakers: Philip Engel, University of Illinois
More: https://www.ias.edu/events/workshop-recent-developments-hodge-theory-and-o-minimality-1
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.
Simonyi Hall 101
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Location
Simonyi Hall 101Speakers
Philip Engel, University of Illinois