Real Structures on Horospherical Varieties

Abstract

We study the equivariant real structures on complex horospherical varieties, generalizing classical results known for toric varieties and flag varieties. We obtain a necessary and sufficient condition for the existence of an equivariant real structure on a given horospherical variety, and we determine the number of equivalence classes of equivariant real structures on horospherical homogeneous spaces. We then apply our results to classifying the equivalence classes of equivariant real structures on smooth projective horospherical varieties of Picard rank 1.