On the classification of normal $G$-varieties with spherical orbits

Kevin Langlois

doi:10.5802/afst.1632

On the classification of normal

G

-varieties with spherical orbits

Kevin Langlois ¹

¹ Mathematisches Institut, Heinrich Heine Universität, 40225 Düsseldorf, Germany

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 2, pp. 271-334.

Résumé
Abstract

Dans cet article, nous étudions la géométrie des opérations de groupes réductifs dans les variétés algébriques. Étant donné un groupe algébrique réductif connexe $G$ , nous élaborons une approche géométrique et combinatoire basée sur la théorie de Luna–Vust pour décrire toute $G$ -variété normale avec orbites sphériques. Cette description comprend le cas classique des variétés sphériques et la théorie des $𝕋$ -variétés introduite récemment par Altmann, Hausen et Süss.

In this article, we investigate the geometry of reductive group actions on algebraic varieties. Given a connected reductive group $G$ , we elaborate on a geometric and combinatorial approach based on Luna–Vust theory to describe every normal $G$ -variety with spherical orbits. This description encompasses the classical case of spherical varieties and the theory of $𝕋$ -varieties recently introduced by Altmann, Hausen, and Süss.

Reçu le : 2017-01-14
Accepté le : 2018-03-27
Publié le : 2020-08-28

DOI : 10.5802/afst.1632

Classification : 14L30, 14M27, 14M25, 13A18
Mots clés : action of algebraic groups, Luna–Vust theory, homogeneous spaces, valuation theory

Affiliations des auteurs :

Kevin Langlois ¹

¹ Mathematisches Institut, Heinrich Heine Universität, 40225 Düsseldorf, Germany

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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Kevin Langlois. On the classification of normal $G$-varieties with spherical orbits. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 2, pp. 271-334. doi : 10.5802/afst.1632. https://afst.centre-mersenne.org/articles/10.5802/afst.1632/

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