Realisation of abelian varieties as automorphism groups

Mathieu Florence

Realisation of abelian varieties as automorphism groups

Algebraic Geometry 2022-05-13 v2

Authors: Mathieu Florence

Abstract

Let $A/F$ be an abelian variety over a field. Does there exist a smooth projective $F$ -variety $X$ , such that $A$ is isomorphic to the automorphism group scheme of $X/F$ ? We show that the answer is positive, if and only if $A$ has only finitely many automorphisms, over an algebraic closure of $F$ . When $F=\mathbb C$ , this result is due to Lombardo and Maffei. When $F$ is algebraically closed, it was obtained independently by Blanc and Brion.

Keywords

abelian variety automorphism group scheme smooth projective variety field algebraic closure

Cite

@article{arxiv.2102.02581,
  title  = {Realisation of abelian varieties as automorphism groups},
  author = {Mathieu Florence},
  journal= {arXiv preprint arXiv:2102.02581},
  year   = {2022}
}

Comments

Improved exposition and proofs. \`A para\^itre aux Annales de la Facult\'e des Sciences de Toulouse

Realisation of abelian varieties as automorphism groups

Abstract

Keywords

Cite

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