Connecting orbits in quasiaffine spherical varieties via $B$-root subgroups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908906352017408 |
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| author | Avdeev, Roman Zhgoon, Vladimir |
| author_facet | Avdeev, Roman Zhgoon, Vladimir |
| contents | Given a connected reductive algebraic group $G$ with a Borel subgroup $B$ and a quasiaffine spherical $G$-variety $X$, we prove that every $G$-orbit $Y$ contained in the regular locus of $X$ can be connected by a $B$-normalized additive one-parameter group action with any minimal $G$-orbit in $X$ containing $Y$ in its closure. As a consequence, we show that the regular locus of $X$ is transitive for the subgroup in the automorphism group of $X$ generated by $G$ and all $B$-normalized additive one-parameter subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09906 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Connecting orbits in quasiaffine spherical varieties via $B$-root subgroups Avdeev, Roman Zhgoon, Vladimir Algebraic Geometry 14R20, 14M27, 14M25, 13N15 Given a connected reductive algebraic group $G$ with a Borel subgroup $B$ and a quasiaffine spherical $G$-variety $X$, we prove that every $G$-orbit $Y$ contained in the regular locus of $X$ can be connected by a $B$-normalized additive one-parameter group action with any minimal $G$-orbit in $X$ containing $Y$ in its closure. As a consequence, we show that the regular locus of $X$ is transitive for the subgroup in the automorphism group of $X$ generated by $G$ and all $B$-normalized additive one-parameter subgroups. |
| title | Connecting orbits in quasiaffine spherical varieties via $B$-root subgroups |
| topic | Algebraic Geometry 14R20, 14M27, 14M25, 13N15 |
| url | https://arxiv.org/abs/2512.09906 |