Flexibility of affine spherical varieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909956960157696 |
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| author | Shafarevich, Anton |
| author_facet | Shafarevich, Anton |
| contents | We prove that the automorphism group $\mathrm{Aut}(X)$ of an affine spherical variety $X$ acts transitively on the set of smooth points $X^{reg}.$ If every invertible regular function on $X$ is constant, we prove that $X$ is flexible, i.e., the subgroup of $\mathrm{Aut}(X)$ generated by all $\mathbb{G}_a$-subgroups acts transitively on $X^{reg}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07031 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Flexibility of affine spherical varieties Shafarevich, Anton Algebraic Geometry 14R20, 14M27, 14M25, 13N15 We prove that the automorphism group $\mathrm{Aut}(X)$ of an affine spherical variety $X$ acts transitively on the set of smooth points $X^{reg}.$ If every invertible regular function on $X$ is constant, we prove that $X$ is flexible, i.e., the subgroup of $\mathrm{Aut}(X)$ generated by all $\mathbb{G}_a$-subgroups acts transitively on $X^{reg}.$ |
| title | Flexibility of affine spherical varieties |
| topic | Algebraic Geometry 14R20, 14M27, 14M25, 13N15 |
| url | https://arxiv.org/abs/2512.07031 |