Sous-groupes algébriques du groupe de Cremona

Abstract

We give a complete classification of maximal algebraic subgroups of the Cremona group of the plane and provide algebraic varieties that parametrize the conjugacy classes. ----- Nous donnons une classification complète des sous-groupes algébriques maximaux du groupe de Cremona du plan et explicitons les variétés qui paramètrent les classes de conjugaison.

Text in French, Translated introduction, 35 pages, 1 figure, to appear in Transform. Groups

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• Infinite algebraic subgroups of the real Cremona group
• The Cremona group is compactly presentable
• Algebraic subgroups of the group of birational transformations of ruled surfaces
• Three chapters on Cremona groups
• Maximal subgroups in the Cremona group
• Some properties of the group of birational maps generated by the automorphisms of ${\mathbb{P}}_{\mathbb{C}}^n$ and the standard involution