On the birational geometry of Schubert varieties

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2015Embargo end date: 01 Jan 2012Publisher:Societe Mathematique de FranceJournal:Bulletin de la Soci&#233;t&#233; math&#233;matique de France, volume 143, pages 489-502 (issn: 0037-9484, eissn: 2102-622X,

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Authors: Schmidt, Benjamin;

doi: 10.24033/bsmf.2696 , 10.48550/arxiv.1208.5507

arXiv: 1208.5507

On the birational geometry of Schubert varieties

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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.

14 pages, v2: Several small corrections. Accepted for publication in "Bulletin de la SMF"

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The Ohio State University
United States

Keywords

14M15 (Primary), 14E30 (Secondary), Schubert varieties, Grassmannians, Schubert varieties, flag manifolds, birational geometry, Mathematics - Algebraic Geometry, small resolutions, FOS: Mathematics, Representation Theory (math.RT), Minimal model program (Mori theory, extremal rays), Algebraic Geometry (math.AG), Mathematics - Representation Theory

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