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no. 4
Abelian varieties as automorphism groups of smooth projective varieties in arbitrary characteristics
Jérémy Blanc1; Michel Brion2
1 Universität Basel, Departement Mathematik und Informatik, Spiegelgasse 1, CH-4051 Basel, Switzerland
2 Université Grenoble Alpes, Institut Fourier, CS 40700, 38058 Grenoble Cedex 9, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 32 (2023) no. 4, pp. 607-622.

Let A be an abelian variety over an algebraically closed field. We show that A is the automorphism group scheme of some smooth projective variety if and only if A has only finitely many automorphisms as an algebraic group. This generalizes a result of Lombardo and Maffei for complex abelian varieties.

Soit A une variété abélienne sur un corps algébriquement clos. Nous montrons que A est le groupe d’automorphismes d’une variété projective lisse si et seulement si A n’a qu’un nombre fini d’automorphismes en tant que groupe algébrique. Ceci généralise un résultat de Lombardo et Maffei pour les variétés abéliennes complexes.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1746
Classification: 14K05, 14J50, 14L30, 14M20
Keywords: Abelian varieties, automorphism group schemes, Albanese morphism

Jérémy Blanc 1; Michel Brion 2

1 Universität Basel, Departement Mathematik und Informatik, Spiegelgasse 1, CH-4051 Basel, Switzerland
2 Université Grenoble Alpes, Institut Fourier, CS 40700, 38058 Grenoble Cedex 9, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Jérémy Blanc; Michel Brion. Abelian varieties as automorphism groups of smooth projective varieties in arbitrary characteristics. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 32 (2023) no. 4, pp. 607-622. doi : 10.5802/afst.1746. https://afst.centre-mersenne.org/articles/10.5802/afst.1746/

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