Microlocal multiplicity of matroid Schubert varieties

TL;DR

This paper investigates the multiplicity of the characteristic cycle of matroid Schubert varieties, revealing it as a combinatorial invariant and providing explicit formulas for its computation, with conjectures extending to arbitrary matroids.

Contribution

It introduces a combinatorial invariant for the multiplicity of matroid Schubert varieties and offers explicit formulas for calculation, advancing understanding of their geometric properties.

Findings

Multiplicity is a combinatorial invariant.

Explicit formulas for multiplicity computation.

Conjecture on non-negativity for general matroids.

Abstract

We study the multiplicity number of the characteristic cycle of the intersection complex of the matroid Schubert variety. It is shown to be a combinatorial invariant, and it can be computed by explicit formulas. We also conjecture that the generalization to arbitrary matroid is non-negative.