Automorphism groups of affine varieties consisting of algebraic elements
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929741545603072 |
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| author | Perepechko, Alexander Regeta, Andriy |
| author_facet | Perepechko, Alexander Regeta, Andriy |
| contents | 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 $G=H.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_08950 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Automorphism groups of affine varieties consisting of algebraic elements Perepechko, Alexander Regeta, Andriy Algebraic Geometry 14R20 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 $G=H.$ |
| title | Automorphism groups of affine varieties consisting of algebraic elements |
| topic | Algebraic Geometry 14R20 |
| url | https://arxiv.org/abs/2203.08950 |