Local rigidity of projective smooth horospherical varieties of Picard number two

TL;DR

This paper investigates the local rigidity of a specific class of smooth horospherical varieties, extending previous work on their automorphism groups to understand their deformation properties.

Contribution

It provides new insights into the local rigidity of projective smooth horospherical varieties of rank one and Picard number two, building upon prior automorphism group computations.

Findings

Identifies conditions under which these varieties are locally rigid.

Extends previous automorphism group results to deformation theory.

Contributes to classification of horospherical varieties based on rigidity.

Abstract

We study the local rigidity of projective smooth horospherical varieties of rank one and Picard number two. These varieties have been already considered by the second author in a work where their automorphism groups are computed. The results given here are a natural continuation of this work.