When is the automorphism group of an affine variety nested?
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866913317291819008 |
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| author | Perepechko, Alexander Regeta, Andriy |
| author_facet | Perepechko, Alexander Regeta, Andriy |
| contents | For an affine algebraic variety $X$, we study the subgroup $\mathrm{Aut}_{\text{alg}}(X)$ of the group of regular automorphisms $\mathrm{Aut}(X)$ of $X$ generated by all the connected algebraic subgroups. We prove that $\mathrm{Aut}_{\text{alg}}(X)$ is nested, i.e., is a direct limit of algebraic subgroups of $\mathrm{Aut}(X)$, if and only if all the $\mathbb{G}_a$-actions on $X$ commute. Moreover, we describe the structure of such a group $\mathrm{Aut}_{\text{alg}}(X)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_07699 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | When is the automorphism group of an affine variety nested? Perepechko, Alexander Regeta, Andriy Algebraic Geometry 14R05, 14R20, 14R25 For an affine algebraic variety $X$, we study the subgroup $\mathrm{Aut}_{\text{alg}}(X)$ of the group of regular automorphisms $\mathrm{Aut}(X)$ of $X$ generated by all the connected algebraic subgroups. We prove that $\mathrm{Aut}_{\text{alg}}(X)$ is nested, i.e., is a direct limit of algebraic subgroups of $\mathrm{Aut}(X)$, if and only if all the $\mathbb{G}_a$-actions on $X$ commute. Moreover, we describe the structure of such a group $\mathrm{Aut}_{\text{alg}}(X)$. |
| title | When is the automorphism group of an affine variety nested? |
| topic | Algebraic Geometry 14R05, 14R20, 14R25 |
| url | https://arxiv.org/abs/1903.07699 |