Matroid psi classes

TL;DR

This paper introduces psi classes in matroid Chow rings, generalizing properties from moduli spaces of curves, and uses them to derive new results on matroid invariants and duality.

Contribution

It defines matroid psi classes and proves their key properties, enabling new proofs of matroid characteristic polynomial coefficients, volume formulas, and Poincare duality.

Findings

Chow-theoretic interpretation of reduced characteristic polynomial coefficients

Explicit formulas for matroid volume polynomials

Poincare duality in matroid Chow rings

Abstract

Motivated by the intersection theory of moduli spaces of curves, we introduce psi classes in matroid Chow rings and prove a number of properties that naturally generalize properties of psi classes in Chow rings of Losev-Manin spaces. We use these properties of matroid psi classes to give new proofs of (1) a Chow-theoretic interpretation for the coefficients of the reduced characteristic polynomials of matroids, (2) explicit formulas for the volume polynomials of matroids, and (3) Poincare duality for matroid Chow rings.