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

By B. Pasquier. 2008

105 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/68abbccfe57eaf26d919b9c4aa8ec9a364b69d66

How researchers see this paper

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In Applied Mathematics

1. Thibaut Delcroix
2. N. Perrin
3. Chenyang Xu
4. Jiyuan Han
5. Chi Li

In Geometry and Topology

1. Thibaut Delcroix
2. N. Perrin
3. Chenyang Xu
4. P. Chaput
5. Jiyuan Han
6. Chi Li

In Mathematical Physics

1. Thibaut Delcroix
2. N. Perrin

Citations in the corpus

• ON THE GEOMETRY OF SPHERICAL VARIETIES (2012, background): “In [118], Pasquier classifies the smooth horospherical varieties with Picard number one.”
• K-stability of Fano spherical varieties (2016, background): “Examples of interesting smooth, Fano, colored horospherical varieties, (thus not treated by [PS10]), are given by Pasquier in [Pas09].”