Connecting orbits in quasiaffine spherical varieties via $B$-root subgroups

Fuente: arXiv
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Autores principales: Avdeev, Roman, Zhgoon, Vladimir
Formato: Preprint
Publicado: 2025
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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.
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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