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Tits alternative in hypek\"ahler manifolds

Research paper by Keiji Oguiso

Indexed on: 24 Apr '05Published on: 24 Apr '05Published in: Mathematics - Algebraic Geometry



Abstract

We show an analogous result of the famous Tits alternative for a group G of birational automorphisms of a projective hyperk\"aher 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.