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.