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.

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 :
Accepté le :
Publié le :
DOI : 10.5802/afst.1632
Classification : 14L30, 14M27, 14M25, 13A18
Mots clés : action of algebraic groups, Luna–Vust theory, homogeneous spaces, valuation theory

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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