On the Birational Geometry of Schubert Varieties

preprint2015arXivOpen access

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.

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