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arXiv · 2512.07031

Flexibility of affine spherical varieties

Anton Shafarevich
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Abstract

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 $X^{reg}.$

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Anton Shafarevich. 2025-12-07. Flexibility of affine spherical varieties. https://arxiv.org/abs/2512.07031

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