Finiteness Results on the Automorphism Groups of Compact Hyperkähler Manifolds
Time: 2018-07-27
Published By: Meng Yu
Speaker(s): Lie Fu (University of Lyon 1)
Time: 14:00-15:00 August 16, 2018
Venue: Room 78201, Jingchunyuan 78, BICMR
Abstract: A Klein automorphism of a complex manifold is by definition a holomorphic or anti-holomorphic diffeomorphism. I present some finiteness results I obtained in recent joint work with Andrea Cattaneo concerning the Klein automorphism groups of compact hyperkähler manifolds. We show that this group, as well as the (holomorphic) automorphism group, has only finitely many finite subgroups up to conjugacy. As an application in real algebraic geometry, we show that a compact hyperkähler manifold admits only finitely many real structures, i.e. anti-holomorphic involutions, up to equivalence. If time permits, I will also answer a question of Prof. Oguiso on the finite generation of automorphism group of a compact hyperkähler manifold: we actually show that it is finitely presented. The preprint is available at arXiv:1806.03864.
