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Variétés horosphériques de Fano

Abstract : A horospherical variety is a normal algebraic variety where a reductive algebraic group acts with an open orbit which is a torus bundle over a flag variety. The dimension of the torus is called the rank of the horospherical variety. For example, toric varieties and flag varieties are horospherical. In this thesis, we classify Fano horospherical varieties in terms of certain rational polytopes that generalize the reflexive polytopes considered by V.Batyrev. Then, we obtain an upper bound on the degree of smooth Fano horospherical varieties, analogus to that given by O.Debarre in the toric case. We extend a recent result of C.Casagrande: the Picard number of any Fano Q-factorial horospherical variety is bounded by twice the dimension. Also, we give several examples in rank 2.
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Contributor : Martine Barbelenet <>
Submitted on : Wednesday, November 29, 2006 - 10:57:36 AM
Last modification on : Wednesday, November 4, 2020 - 1:54:04 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 7:34:30 PM


  • HAL Id : tel-00116977, version 1



Boris Pasquier. Variétés horosphériques de Fano. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2006. Français. ⟨tel-00116977⟩



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