Toricness and smoothness criteria for spherical varieties
Algebraic Geometry
2026-01-13 v1 Representation Theory
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.
Cite
@article{arxiv.2601.06376,
title = {Toricness and smoothness criteria for spherical varieties},
author = {Giuliano Gagliardi and Johannes Hofscheier and Heath Pearson},
journal= {arXiv preprint arXiv:2601.06376},
year = {2026}
}
Comments
The results of this paper originally appeared as part of arXiv:2502.21155v1