Tits alternative in hypekähler manifolds

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 group of the so-called singular K3 surface contains a non-commutative free group.

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Published 1 January 2006