no. 3
On the birational geometry of Schubert varieties
[Sur la géométrie birationnelle des variétés de Schubert]
Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 3, pp. 489-502

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.

Nous décrivons toutes les petites contractions de Mori des variétés de Schubert (co)minuscules en utilisant leur structure d'espace de rêve de Mori (Mori dream space). Nous en déduisons une description de toutes les résolutions IH-petites des variétés de Schubert (co)minuscules et généralisons ainsi les résultats de Perrin : nous étendonds ses résultats à tout corps algebriquement clos de caracteristique quelconque et aux variétés de Schubert cominuscules. En outre, l'utilisation des petites contractions des espaces de rêve de Mori simplifie grandement les arguments.

Publié le :
DOI : 10.24033/bsmf.2696
Classification : 14M15, 14E30
Keywords: Schubert varieties, birational geometry, small resolutions 
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     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {489--502},
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     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {143},
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Schmidt, Benjamin. On the birational geometry of Schubert varieties. Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 3, pp. 489-502. doi: 10.24033/bsmf.2696

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