Horospherical varieties with quotient singularities

TL;DR

This paper provides a combinatorial criterion to identify when horospherical varieties have quotient singularities and demonstrates that such varieties are globally quotients of smooth varieties by finite abelian groups.

Contribution

It introduces a new combinatorial characterization for quotient singularities in horospherical varieties and establishes their global quotient structure.

Findings

Characterization of quotient singularities via combinatorics

Every quasiprojective horospherical variety with quotient singularities is a global quotient

Provides criteria to identify quotient singularities in horospherical varieties

Abstract

Our main result is a combinatorial characterization of when a horospherical variety has (at worst) quotient singularities. Using this characterization, we show that every quasiprojective horospherical variety with quotient singularities is globally the quotient of a smooth variety by a finite abelian group.