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

Nikon Kurnosov, Egor Yasinsky

Published 2018-10-23Version 1

We study groups of bimeromorphic and biholomorphic automorphisms of projective hyperk\"ahler 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.