Singularities of divisors on flag varieties via Hwang's product theorem

TL;DR

This paper provides an alternative proof of a recent result characterizing when pairs of flag varieties and divisors are Kawamata log terminal, using Hwang's product theorem.

Contribution

It offers a new proof of Pasquier's result on singularities of divisors on flag varieties, enhancing understanding of their geometric properties.

Findings

Pairs (X,D) are Kawamata log terminal iff the divisor D has no integral part.

The proof utilizes Hwang's product theorem to analyze singularities.

Clarifies the relationship between divisor stability and singularity types on flag varieties.

Abstract

We give an alternative proof of a recent result by Pasquier stating that for a generalized flag variety $X=G/P$ and an effective $\mathbb{Q}$-divisor $D$ stable with respect to a Borel subgroup the pair $(X,D)$ is Kawamata log terminal if and only if $\lfloor D\rfloor=0$.