On frobenius splitting of orbit closures of spherical subgroups in flag varieties

TL;DR

This paper establishes criteria for the geometric and cohomological properties of orbit closures of spherical subgroups in flag varieties, using Frobenius splitting and global F-regularity techniques.

Contribution

It introduces new criteria for orbit closures to be Frobenius split and globally F-regular, enhancing understanding of their geometric structure.

Findings

Orbit closures are Frobenius split under certain conditions.

Orbit closures exhibit global F-regularity when criteria are met.

Results improve understanding of singularities and cohomology of orbit closures.

Abstract

Let $H$ be a connected spherical subgroup of a semisimple algebraic group $G$. In this paper, we give a criterion for $H$-orbit closures in the flag variety of $G$ to have nice geometric and cohomological properties. Our main tool is the method of Frobenius splitting and of global F-regularity.