# Horospherical stacks

## TL;DR

This paper establishes structure theorems for algebraic stacks with reductive group actions, generalizing known results for toric stacks and providing new examples of algebraic stacks as global quotients.

## Contribution

It extends the theory of algebraic stacks with group actions to include horospherical stacks, broadening the class of known algebraic stacks with such structures.

## Key findings

- Proved structure theorems for horospherical stacks
- Identified conditions under which these stacks are global quotients
- Generalized previous results for toric stacks

## Abstract

We prove structure theorems for algebraic stacks with a reductive group action and a dense open substack isomorphic to a horospherical homogeneous space, and thereby obtain new examples of algebraic stacks which are global quotient stacks. Our results partially generalize the work of Fantechi-Mann-Nironi and Geraschenko-Satriano for abstract toric stacks.