Kumar's criterion modulo p

TL;DR

This paper introduces a combinatorial criterion using equivariant multiplicities to determine p-smoothness of attractive fixed points on T-varieties, applicable to Schubert varieties across all primes p.

Contribution

It provides a novel criterion based on equivariant multiplicities to identify p-smooth points on Schubert varieties, extending the understanding of their geometric properties.

Findings

Equivariant multiplicities can determine p-smoothness of fixed points.

The criterion applies uniformly for all primes p.

It offers a combinatorial approach to study Schubert varieties.

Abstract

We prove that equivariant multiplicities may be used to determine whether attractive fixed points on T-varieties are p-smooth. This gives a combinatorial criterion for the determination of the p-smooth locus of Schubert varieties for all primes p.