Characterizing smooth affine spherical varieties via the automorphism group
[Caractérisation des variétés sphériques affines lisses par le groupe des automorphismes]
Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 379-414.

Soit G un groupe réductif connexe. Nous montrons que le monoïde des poids d’une variété G-sphérique quasi-affine est déterminé par les poids de ses 𝔾 a -actions non triviales homogènes sous l’action d’un sous-groupe de Borel de G. Comme application, nous obtenons qu’une variété sphérique affine lisse non isomorphe à un tore est déterminée par son groupe des automorphismes (considéré comme un ind-groupe) dans la catégorie des variétés irréductibles affines lisses.

Let G be a connected reductive algebraic group. We prove that for a quasi-affine G-spherical variety the weight monoid is determined by the weights of its non-trivial 𝔾 a -actions that are homogeneous with respect to a Borel subgroup of G. As an application we get that a smooth affine spherical variety that is non-isomorphic to a torus is determined by its automorphism group (considered as an ind-group) inside the category of smooth affine irreducible varieties.

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Accepté le :
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DOI : 10.5802/jep.149
Classification : 14R20, 14M27, 14J50, 22F50
Keywords: Automorphism groups of quasi-affine varieties, quasi-affine spherical varieties, root subgroups, quasi-affine toric varieties
Mot clés : Groupes des automorphismes des variétés quasi-affines, variétés sphériques quasi-affines, sous-groupes de racines, variétés toriques quasi-affines
Andriy Regeta 1 ; Immanuel van Santen 2

1 Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität Jena Ernst-Abbe-Platz 2, DE-07743 Jena, Germany
2 Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, CH-4051 Basel, Switzerland
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Andriy Regeta; Immanuel van Santen. Characterizing smooth affine spherical varieties via the automorphism group. Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 379-414. doi : 10.5802/jep.149. https://jep.centre-mersenne.org/articles/10.5802/jep.149/

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