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

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Abstract

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.

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  1. Hausdorff Center for Mathematics, Villa Maria, Endenicher Allee 62, 53115, Bonn, Germany

    Boris Pasquier

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  1. Boris Pasquier
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Pasquier, B. On some smooth projective two-orbit varieties with Picard number 1. Math. Ann. 344, 963–987 (2009). https://doi.org/10.1007/s00208-009-0341-9

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  • DOI: https://doi.org/10.1007/s00208-009-0341-9

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