Tautological classes of matroids
Combinatorics
2023-04-17 v4 Algebraic Geometry
Abstract
We introduce certain torus-equivariant classes on permutohedral varieties which we call "tautological classes of matroids" as a new geometric framework for studying matroids. Using this framework, we unify and extend many recent developments in matroid theory arising from its interaction with algebraic geometry. We achieve this by establishing a Chow-theoretic description and a log-concavity property for a 4-variable transformation of the Tutte polynomial, and by establishing an exceptional Hirzebruch-Riemann-Roch-type formula for permutohedral varieties that translates between K-theory and Chow theory.
Keywords
Cite
@article{arxiv.2103.08021,
title = {Tautological classes of matroids},
author = {Andrew Berget and Christopher Eur and Hunter Spink and Dennis Tseng},
journal= {arXiv preprint arXiv:2103.08021},
year = {2023}
}
Comments
71 pages; comments welcome. v4: minor edits. To appear in Invent. Math