On the Birational Geometry of Schubert Varieties

TL;DR

This paper classifies all Q-factorializations and IH-small resolutions of (co)minuscule Schubert varieties using their Mori dream space structure, extending previous results to positive characteristic fields and simplifying the approach.

Contribution

It provides a complete classification of Q-factorializations and IH-small resolutions for (co)minuscule Schubert varieties, generalizing and simplifying prior work.

Findings

Classified all Q-factorializations of (co)minuscule Schubert varieties.

Described all IH-small resolutions for these varieties.

Extended results to positive characteristic fields.

Abstract

We classify all Q-factorializations of (co)minuscule Schubert varieties by using their Mori dream space structure. As a corollary we obtain a description of all IH-small resolutions of (co)minuscule Schubert varieties generalizing results of Perrin. We improve his results by including algebraically closed fields of positive characteristic and cominuscule Schubert varieties. Moreover, the use of Q-factorializations and Mori dream spaces simplifies the arguments substantially.