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

2018/10/23 by Nikon Kurnosov, Egor Yasinsky, Kurnosov, Nikon +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #Metric Geometry (math.MG) #math.AG #math.GR #math.MG

paper · pdf · doi:10.48550/arxiv.1810.09730

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

openalex publication_date 2018/10/23 · arxiv created 2019/01/28 · arxiv updated 2019/01/29 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28

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.

Related

• Bimeromorphic automorphism groups of non-projective hyperkähler manifolds - a note inspired by C. T. McMullen
• Tits alternative in hypekähler manifolds
• Hyperbolic 2-dimensional manifolds with 3-dimensional automorphism groups
• Automorphisms of hyperkähler manifolds in the view of topological entropy
• Finite groups of symplectic automorphisms of hyperkähler manifolds of type K3^[2]