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Compactification d'espaces homogènes sphériques sur un corps quelconque

Abstract : This thesis is devoted to the study of embeddings of spherical homogeneous spaces over an arbitrary field. In the first part, we address the classification of such embeddings, in the spirit of Demazure and many others in the setting of toric varieties and of Luna, Vust and Knop in the setting of spherical varieties. In the second part, we generalize in positive characteristics some results obtained by Bien and Brion on those complete smooth embeddings that are log homogeneous, i.e., whose boundary is a normal crossing divisor and the associated logarithmic tangent bundle is generated by its global sections. In the last part, we construct an explicit smooth log homogeneous compactification of the general linear group by successive blow-ups (different from the one obtained by Kausz). By taking fixed points of certain automorphisms on this compactification, one gets smooth log homogeneous compactifications of some classical semi-simple groups.
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Submitted on : Tuesday, July 10, 2012 - 2:41:09 PM
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Mathieu Huruguen. Compactification d'espaces homogènes sphériques sur un corps quelconque. Mathématiques générales [math.GM]. Université de Grenoble, 2011. Français. ⟨NNT : 2011GRENM068⟩. ⟨tel-00716402⟩



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