Smooth projective horospherical varieties with Picard number 1

TL;DR

This paper classifies smooth projective horospherical varieties with Picard number 1, analyzes their automorphism groups, and characterizes non-homogeneous cases through geometric properties.

Contribution

It provides a complete description of such varieties, including automorphism group actions and criteria for non-homogeneity, advancing understanding in algebraic geometry.

Findings

Automorphism groups act with at most two orbits on these varieties.

A geometric characterization of non-homogeneous varieties is established.

Classification of smooth projective horospherical varieties with Picard number 1.

Abstract

We describe smooth projective horospherical varieties with Picard number 1. Moreover we prove that the automorphism group of any such variety acts with at most two orbits and we give a geometric characterisation of non-homogeneous ones.