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

Details On some smooth projective two-orbits varieties with Picard number 1 On some smooth projective two-orbits varieties with Picard number 1

2008-01-23

arxiv.org/abs/0801.3534v1

Mathematics

Algebraic Geometry

32 pages

Scientific paper

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

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