A combinatorial smoothness criterion for spherical varieties

TL;DR

This paper introduces a combinatorial criterion to determine the smoothness of any spherical variety, expanding previous results specifically for type A varieties by leveraging the classification of multiplicity-free spaces.

Contribution

It generalizes an earlier smoothness criterion for type A spherical varieties to all spherical varieties using a combinatorial approach.

Findings

Provides a new combinatorial criterion for smoothness

Extends previous results from type A to all spherical varieties

Utilizes classification of multiplicity-free spaces

Abstract

We suggest a combinatorial criterion for the smoothness of an arbitrary spherical variety using the classification of multiplicity-free spaces, generalizing an earlier result of Camus for spherical varieties of type $A$.