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arXiv · 2203.08950

Automorphism groups of affine varieties consisting of algebraic elements

Alexander Perepechko·Andriy Regeta
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Abstract

Given an affine algebraic variety $X$, we prove that if the neutral component $\mathrm{Aut}^\circ(X)$ of the automorphism group consists of algebraic elements, then it is nested, i.e., is a direct limit of algebraic subgroups. This improves our earlier result. To prove it, we obtain the following fact. If a connected ind-group $G$ contains a closed connected nested ind-subgroup $H\subset G$, and for any $g\in G$ some positive power of $g$ belongs to $H$, then $G=H.$

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Alexander Perepechko, Andriy Regeta. 2022-03-16. Automorphism groups of affine varieties consisting of algebraic elements. https://doi.org/10.1090/proc/16759

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