Automorphisms of hyperk\"ahler manifolds and groups acting on CAT(0) spaces
Algebraic Geometry
2019-01-29 v2 Group Theory
Metric Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1810.09730,
title = {Automorphisms of hyperk\"ahler manifolds and groups acting on CAT(0) spaces},
author = {Nikon Kurnosov and Egor Yasinsky},
journal= {arXiv preprint arXiv:1810.09730},
year = {2019}
}
Comments
Minor changes. Remark 2.3, some definitions from metric geometry and references added; a couple of inaccuracies fixed. All the main results unchanged