K-classes of matroids and equivariant localization

Abstract

To every matroid, we associate a class in the K-theory of the Grassmannian. We study this class using the method of equivariant localization. In particular, we provide a geometric interpretation of the Tutte polynomial. We also extend results of the second author concerning the behavior of such classes under direct sum, series and parallel connection and two-sum; these results were previously only established for realizable matroids, and their earlier proofs were more difficult.

v2: added a starting point for combinatorialists in Section 2.4, + minor changes

Cited by in corpus (14)

• Chern-Schwartz-MacPherson cycles of matroids
• Valuative invariants for large classes of matroids
• Projected Richardson varieties and affine Schubert varieties
• Grothendieck classes of quiver cycles as iterated residues
• Gorenstein graphic matroids from multigraphs
• The Universal Valuation of Coxeter Matroids
• Foundations of Boij-Söderberg Theory for Grassmannians
• Equivariant K-theory classes of matrix orbit closures
• Orbits in $({\mathbb{P}}^r{)}^n$ and equivariant quantum cohomology
• The tropical Poincaré-Hopf theorem
• Schubert matroids, Delannoy paths, and Speyer's invariant
• Patch ideals and Peterson varieties
• Matroids and the space of torus-invariant subvarieties of the Grassmannian with given homology class
• Equivariant Tutte Polynomial