Real structures on horospherical varieties

Structures réelles sur des variétés horosphériques

Lucy Moser-Jauslin (1) , Ronan Terpereau (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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.

Domaines: Géométrie algébrique [math.AG]

Lucy Moser-Jauslin, Ronan Terpereau. Real structures on horospherical varieties. Michigan Mathematical Journal, 2022, 71 (2), pp.283 - 320. ⟨10.1307/mmj/20195793⟩. ⟨hal-01865442v2⟩