What question did this study set out to answer?

This research aims to explore the multiplicity numbers associated with the characteristic cycles in matroid Schubert varieties.

March 25, 2026

Microlocal Multiplicity of Matroid Schubert Varieties

Key Points

This research aims to explore the multiplicity numbers associated with the characteristic cycles in matroid Schubert varieties.
Studied the characteristic cycle of intersection complexes of matroid Schubert varieties.
Formulated explicit formulas for computing multiplicity numbers.
Proposed a conjecture regarding the non-negativity of multiplicity in arbitrary matroids.
Demonstrated that multiplicity numbers serve as a combinatorial invariant.
Established explicit formulas to calculate multiplicity numbers.
Conjectured non-negativity of the multiplicity for more general matroid structures.

Abstract

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 can be computed by explicit formulas. We also conjecture that the generalization to an arbitrary matroid is non-negative.

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