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

2021/02/04 by Blanc, Jérémy, Brion, Michel
#14J50 #14K05 #14L30 #14M20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.02459

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.

Related

• Realisation of abelian varieties as automorphism groups
• Abelian varieties as automorphism groups of smooth projective varieties
• Realisation of linear algebraic groups as automorphism groups
• Algebraic groups as automorphism groups of algebras
• Automorphism groups of almost homogeneous varieties