Mathematics > Algebraic Geometry
[Submitted on 11 Jun 2018 (v1), last revised 5 Aug 2019 (this version, v3)]
Title:Finiteness of Klein actions and real structures on compact hyperkähler manifolds
View PDFAbstract:One central problem in real algebraic geometry is to classify the real structures of a given complex manifold. We address this problem for compact hyperkähler manifolds by showing that any such manifold admits only finitely many real structures up to equivalence. We actually prove more generally that there are only finitely many, up to conjugacy, faithful finite group actions by holomorphic or anti-holomorphic automorphisms (the so-called Klein actions). In other words, the automorphism group and the Klein automorphism group of a compact hyperkähler manifold contain only finitely many conjugacy classes of finite subgroups. We furthermore answer a question of Oguiso by showing that the automorphism group of a compact hyperkähler manifold is finitely presented.
Submission history
From: Lie Fu [view email][v1] Mon, 11 Jun 2018 08:50:26 UTC (39 KB)
[v2] Mon, 4 Mar 2019 20:39:04 UTC (41 KB)
[v3] Mon, 5 Aug 2019 03:57:00 UTC (42 KB)
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