For an affine algebraic variety X, we study the subgroup Aut_alg(X) of the group of regular automorphisms Aut(X) of X generated by all the connected algebraic subgroups. We prove that Aut_alg(X) is nested, i.e., is a direct limit of algebraic subgroups of Aut(X), if and only if all the 𝔾_a-actions on X commute. Moreover, we describe the structure of such a group Aut_alg(X).
When is the automorphism group of an affine variety nested?
Andriy Regeta
2023
Abstract
For an affine algebraic variety X, we study the subgroup Aut_alg(X) of the group of regular automorphisms Aut(X) of X generated by all the connected algebraic subgroups. We prove that Aut_alg(X) is nested, i.e., is a direct limit of algebraic subgroups of Aut(X), if and only if all the 𝔾_a-actions on X commute. Moreover, we describe the structure of such a group Aut_alg(X).
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