Tits alternative in hypekähler manifolds

Abstract

We show an analogous result of the famous Tits alternative for a group G of birational automorphisms of a projective hyperkäher manifold: Either G contains a non-commutative free group or G is an almost abelian group of finite rank. As an application, we show that the automorphism groups of the so-called singular K3 surfaces contain non-commutative free groups.

9pages; all the previous results have been generalized and accordingto this the title has been changed

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• Higher dimensional Enriques varieties and automorphisms of generalized Kummer varieties
• Conjecture of Tits type for complex varieties and Theorem of Lie-Kolchin type for a cone
• Mordell-Weil groups of a hyperkähler manifold - a question of F. Campana