2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146475We classify all smooth projective horospherical varieties with Picard number 1. We prove that the automorphism group of any such variety X acts with at most two orbits and that this group still acts with only two orbits on X blown up at the closed orbit. We characterize all smooth projective two-orbits varieties with Picard number 1 that satisfy this latter property.32 pagesAlgebraic Geometry14J45, 14L30, 14M17text