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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. For example, toric varieties and flag varieties are horospherical. In this paper, 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, several examples are given in rank 2.
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https://tel.archives-ouvertes.fr/tel-00111912
Contributor : Boris Pasquier <>
Submitted on : Monday, November 6, 2006 - 3:28:52 PM
Last modification on : Wednesday, November 4, 2020 - 1:51:34 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 9:37:35 PM

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  • HAL Id : tel-00111912, version 1

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Boris Pasquier. Variétés horosphériques de Fano. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2006. Français. ⟨tel-00111912⟩

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