Real structures on horospherical varieties

TL;DR

This paper investigates the existence and classification of equivariant real structures on complex horospherical varieties, extending known results from toric and flag varieties to a broader class.

Contribution

It provides a necessary and sufficient condition for the existence of equivariant real structures and classifies them for smooth projective horospherical varieties of Picard rank 1.

Findings

Established criteria for real structures on horospherical varieties

Determined the number of equivalence classes of such structures

Classified real structures on specific smooth projective cases

Abstract

We study the equivariant real structures on complex horospherical varieties, generalizing classical results known for toric varieties and flag varieties. In particular, we obtain a necessary and sufficient condition for the existence of such real structures and determine the number of equivalence classes. We then apply our results to classify the equivariant real structures on smooth projective horospherical varieties of Picard rank 1.