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Families of commuting automorphisms, and a characterization of the affine space
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 145, Number 2, April 2023
- pp. 413-434
- 10.1353/ajm.2023.0009
- Article
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abstract:
We prove that the affine space of dimension $n\geq 1$ over an uncountable algebraically closed field ${\bf k}$ is determined, among connected affine varieties, by its automorphism group (viewed as an abstract group). The proof is based on a new result concerning algebraic families of pairwise commuting automorphisms.