## Finiteness Results on the Automorphism Groups of Compact Hyperk?hler Manifolds

2018-08-16 14:00 - 2018-08-16 15:00 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 hyperk?hler 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 hyperk?hler 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 hyperk?hler manifold: we actually show that it is finitely presented. The preprint is available at arXiv:1806.03864.<\/span>