Singular loci of Bruhat-Hibi toric varieties

TL;DR

This paper characterizes the singular locus of Bruhat-Hibi toric varieties linked to Schubert varieties in minuscule G/P, revealing it is pure of codimension 3 and describing it via polyhedral faces.

Contribution

It provides a detailed description of the singular locus of these specific toric varieties and establishes its pure codimension, connecting algebraic geometry with polyhedral combinatorics.

Findings

Singular locus described via faces of the associated polyhedral cone

Singular locus is pure of codimension 3 in the variety

Explicit geometric characterization of singular points

Abstract

For the toric variety X associated to the Bruhat poset of Schubert varieties in a minuscule G/P, we describe the singular locus in terms of the faces of the associated polyhedral cone. We further show that the singular locus is pure of codimension 3 in X.