Toricness and smoothness criteria for spherical varieties
Abstract
We prove equivalent numerical conditions for a complete spherical variety to admit a toric structure, and for the smoothness of an arbitrary spherical variety along any given G-orbit. The conditions are in terms of spherical skeletons, a coarse ''subset'' of the Luna-Vust data of a spherical variety. Our smoothness criterion improves upon classical criteria by removing the dependency on external reference tables.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Geometry and complex manifolds
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 10 January 2026
- Document type
- Preprint