# Sur les groupes de transformations birationnelles des surfaces | Annals of Mathematics

Abstract Nous étudions les groupes de type fini agissant par transformations birationnelles sur les surfaces complexes compactes kählériennes. Nous montrons (a) que le groupe des transformations birationnelles d’une surface satisfait l’alternative de Tits, (b) que les actions birationnelles de groupes de Kazhdan sur les surfaces sont toutes birationnellement conjuguées à des actions homographiques sur le plan projectif et (c) que si f et g sont deux transformations birationnelles de surfaces qui commutent, alors ou bien f préserve un pinceau de courbes, ou bien l’un des itérés gm de g, m>0, coïncide avec un itéré fn de f, n∈Z. Let S be any compact complex kähler surface and

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### 数学年刊（Annals of Mathematics）

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