Abelian varieties as automorphism groups of smooth projective varieties in arbitrary characteristics

Jérémy Blanc; Michel Brion

Abelian varieties as automorphism groups of smooth projective varieties in arbitrary characteristics

Algebraic Geometry 2021-05-24 v2

Authors: Jérémy Blanc , Michel Brion

Abstract

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.

Keywords

abelian varieties automorphism groups smooth projective varieties arbitrary characteristics algebraic group

Cite

@article{arxiv.2102.02459,
  title  = {Abelian varieties as automorphism groups of smooth projective varieties in arbitrary characteristics},
  author = {Jérémy Blanc and Michel Brion},
  journal= {arXiv preprint arXiv:2102.02459},
  year   = {2021}
}

Comments

15 pages

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