On some smooth projective two-orbit varieties with Picard number 1

Boris Pasquier (1, 2)

1 IF - Institut Fourier
2 HCM - Hausdorff Center for Mathematics

We 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-orbit varieties with Picard number 1 that satisfy this latter property.

Domaines: Géométrie algébrique [math.AG]

Boris Pasquier. On some smooth projective two-orbit varieties with Picard number 1. Mathematische Annalen, 2009, pp.963-987. ⟨10.1007/s00208-009-0341-9⟩. ⟨hal-00789984⟩