2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74804We 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 changedAlgebraic Geometry14J28, 14J50, 20E05text