Koszul Property and Frobenius Splitting of Schubert Varieties

TL;DR

This paper demonstrates that the Frobenius splitting method can be used to establish the Koszul property of the projective coordinate rings of Schubert varieties, linking algebraic geometry and commutative algebra techniques.

Contribution

It introduces a novel application of Frobenius splitting to prove the Koszul property of Schubert varieties' coordinate rings.

Findings

Frobenius splitting implies Koszul property for Schubert varieties.

Establishes a new connection between Frobenius splitting and algebraic properties.

Provides a method to analyze the algebraic structure of Schubert varieties.

Abstract

We show how the Frobenius splitting method of Mehta-Ramanathan implies the Koszul property of projective coordinate rings of Schubert varieties.