A description of the sarkisov program of horospherical varieties via moment polytopes

TL;DR

This paper explores the Sarkisov program for horospherical varieties, demonstrating how birational equivariant maps between such spaces can be decomposed via moment polytopes.

Contribution

It provides a novel description of the horospherical Sarkisov program using moment polytopes, extending the understanding of birational geometry in this context.

Findings

Establishes a horospherical Sarkisov program framework

Shows the relation between birational maps and moment polytopes

Provides tools for analyzing birational equivalences of horospherical varieties

Abstract

Let X and Y be horospherical Mori fibre spaces which are birational equivariantly with respect to the group action. Then, there is a horospherical Sarkisov program from X/S to Y /T .