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arXiv · 2601.06376

Toricness and smoothness criteria for spherical varieties

Giuliano Gagliardi·Johannes Hofscheier·Heath Pearson
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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.

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Giuliano Gagliardi, Johannes Hofscheier, Heath Pearson. 2026-01-10. Toricness and smoothness criteria for spherical varieties. https://arxiv.org/abs/2601.06376

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