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.

Reçu le :
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DOI : https://doi.org/10.5802/jep.149
Classification : 14R20,  14M27,  14J50,  22F50
Mots clés : Groupes des automorphismes des variétés quasi-affines, variétés sphériques quasi-affines, sous-groupes de racines, variétés toriques quasi-affines
@article{JEP_2021__8__379_0,
     author = {Andriy Regeta and Immanuel van Santen},
     title = {Characterizing smooth affine spherical varieties via the automorphism group},
     journal = {Journal de l'\'Ecole polytechnique --- Math\'ematiques},
     pages = {379--414},
     publisher = {\'Ecole polytechnique},
     volume = {8},
     year = {2021},
     doi = {10.5802/jep.149},
     language = {en},
     url = {https://jep.centre-mersenne.org/item/JEP_2021__8__379_0/}
}
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/item/JEP_2021__8__379_0/

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