# Smooth projective horospherical varieties of Picard group $\mathbb{Z}^2$

## TL;DR

This paper classifies all smooth projective horospherical varieties with Picard group isomorphic to ^2 and explores their geometry using the Log Minimal Model Program, providing foundational insights into their structure.

## Contribution

It offers the first complete classification of these varieties and describes their geometry through the Log Minimal Model Program.

## Key findings

- Complete classification of smooth projective horospherical varieties with Picard group ^2
- Description of their geometric structure via the Log Minimal Model Program
- Establishment of foundational understanding for further geometric analysis

## Abstract

We classify all smooth projective horospherical varieties of Picard group $\mathbb{Z}^2$ and we give a first description of their geometry via the Log Minimal Model Program.