Seshadri stratification for Schubert varieties and Standard Monomial Theory

TL;DR

This paper explores Seshadri stratifications on Schubert varieties, demonstrating their compatibility with existing standard monomial theory to provide a new geometric approach for these varieties.

Contribution

It introduces a new geometric framework for Schubert varieties using Seshadri stratifications, aligning with established standard monomial theory.

Findings

Seshadri stratifications can be applied to Schubert varieties.

Compatibility established between Seshadri stratifications and standard monomial theory.

Provides a new geometric perspective for studying Schubert varieties.

Abstract

The theory of Seshadri stratifications has been developed by the authors with the intention to build up a new geometric approach towards a standard monomial theory for embedded projective varieties with certain nice properties. In this article, we investigate the Seshadri stratification on a Schubert variety arising from its Schubert subvarieties. We show that the standard monomial theory developed in [32] is compatible with this new strategy.