The Log Minimal Model Program for horospherical varieties via moment polytopes

TL;DR

This paper extends the Log Minimal Model Program to pairs involving projective horospherical varieties, using moment polytopes to describe the process, building on prior work on horospherical varieties.

Contribution

It generalizes previous results to include pairs $(X, D)$, providing a framework for the Log MMP in the context of horospherical varieties.

Findings

Describes the Log MMP for pairs $(X, D)$ with horospherical varieties.

Uses moment polytopes to track the MMP process.

Provides a summarized and generalized approach based on earlier work.

Abstract

In a previous work, we described the Minimal Model Program in the family of $\Qbb$-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical varieties. Here, we summarize the results of the previous work and we explain how to generalize them in order to describe the Log Minimal Model Program for pairs $(X,\D)$ when $X$ is a projective horospherical variety.