Automorphisms of hyperkähler manifolds and groups acting on CAT(0) spaces

Abstract

We study groups of bimeromorphic and biholomorphic automorphisms of projective hyperkähler manifolds. Using an action of these groups on some non-positively curved space, we deduce many of their properties, including finite presentation, strong form of Tits' alternative and some structural results about groups consisting of transformations with infinite order.

Minor changes. Remark 2.3, some definitions from metric geometry and references added; a couple of inaccuracies fixed. All the main results unchanged