Simplicial generation of Chow rings of matroids

Chris Eur (Stanford)

04-Sep-2020, 19:00-20:00 (2 years ago)

Abstract: We present a new set of generators for the Chow ring of a matroid. We show that these generators behave like base-point-free divisors by establishing that (i) they correspond to matroid operations that combinatorially mirror hyperplane pullbacks, and (ii) the volume polynomial with respect to these generators satisfies Hodge-type inequalities. We thereby generalize Postnikov's results on generalized permutohedra, and also give a simplified proof of the combinatorially relevant portion of the Hodge theory of matroids developed by Adiprasito-Huh-Katz. No knowledge of matroids will be assumed. This is joint work with Spencer Backman and Connor Simpson.

algebraic geometry

Audience: researchers in the topic

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