English

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