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

Langlois, Kevin

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

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.

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.

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

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