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arXiv · 2511.08489

On the orbit space of a maximal compact subgroup on a spherical homogeneous variety

Dmitry A. Timashev
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Abstract

Let $X=G/H$ be a spherical homogeneous variety for a complex reductive algebraic group $G$. We prove that the orbit space of $X$ under the action of a maximal compact subgroup $K\subset G$ is homeomorphic to the valuation cone of $X$. We also discuss the relation between the orbit type stratification of the orbit space and the face stratification of the valuation cone.

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Dmitry A. Timashev. 2025-11-11. On the orbit space of a maximal compact subgroup on a spherical homogeneous variety. https://arxiv.org/abs/2511.08489

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