We prove that the affine space of dimension n >= 1 over an uncountable algebraically closed field k is determined, among connected affine varieties, by its automorphism group (viewed as an ab-stract group). The proof is based on a new result concerning algebraic families of pairwise commuting automorphisms.
FAMILIES OF COMMUTING AUTOMORPHISMS, AND A CHARACTERIZATION OF THE AFFINE SPACE
Regeta A.
Membro del Collaboration Group
;
2023
Abstract
We prove that the affine space of dimension n >= 1 over an uncountable algebraically closed field k is determined, among connected affine varieties, by its automorphism group (viewed as an ab-stract group). The proof is based on a new result concerning algebraic families of pairwise commuting automorphisms.
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