Multiplicity on a Richardson variety in a cominuscule G/P

TL;DR

This paper proves that in a cominuscule partial flag variety, the multiplicity of a point on a Richardson variety equals the product of its multiplicities on the intersecting Schubert varieties, revealing a multiplicative property.

Contribution

It establishes a new multiplicative relationship for point multiplicities on Richardson varieties in cominuscule G/P, extending understanding of their geometric structure.

Findings

Multiplicity of a point on a Richardson variety equals the product of multiplicities on Schubert varieties

The result applies specifically to cominuscule partial flag varieties

Provides a new tool for studying singularities in algebraic geometry

Abstract

We show that in a cominuscule partial flag variety G/P, the multiplicity of an arbitrary point on a Richardson variety X_w^v = X_w \cap X^v is the product of its multiplicities on the Schubert varieties X_w and X^v.