On the orbit space of a maximal compact subgroup on a spherical homogeneous variety
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909898468491264 |
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| author | Timashev, Dmitry A. |
| author_facet | Timashev, Dmitry A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08489 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the orbit space of a maximal compact subgroup on a spherical homogeneous variety Timashev, Dmitry A. Algebraic Geometry Complex Variables Symplectic Geometry 14M17, 14M27, 57S15 (Primary) 32Q15, 53D20 (Secondary) 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. |
| title | On the orbit space of a maximal compact subgroup on a spherical homogeneous variety |
| topic | Algebraic Geometry Complex Variables Symplectic Geometry 14M17, 14M27, 57S15 (Primary) 32Q15, 53D20 (Secondary) |
| url | https://arxiv.org/abs/2511.08489 |