Realisation of abelian varieties as automorphism groups

2021/02/04 by Mathieu Florence, Florence, Mathieu
Mathematics · Medicine · #Algebraic Geometry and Number Theory #Meromorphic and Entire Functions #Magnolia and Illicium research

paper · pdf · doi:10.48550/arxiv.2102.02581

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.

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