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Strongly Jordan property and free actions of non-abelian free groups

Part of: Automorphic functions Surfaces and higher-dimensional varieties Complex spaces with a group of automorphisms

Published online by Cambridge University Press:  11 August 2022

Jin Hong Kim
Jin Hong Kim*
Affiliation:
Department of Mathematics Education, Chosun University, 309 Pilmun-daero, Dong-gu, Gwangju, 61452, Republic of Korea ([email protected])
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Abstract

Let $X$ be a connected complex manifold and let $Z$ be a compact complex subspace of $X$. Assume that ${\rm Aut}(Z)$ is strongly Jordan. In this paper, we show that the automorphism group ${\rm Aut}(X,\, Z)$ of all biholomorphisms of $X$ preserving $Z$ is strongly Jordan. A similar result has been proved by Meng et al. for a compact Kähler submanifold $Z$ of $X$ instead of a compact complex subspace $Z$ of $X$. In addition, we also show some rigidity result for free actions of large groups on complex manifolds.

Keywords

Jordan propertystrongly JordanJordan constantsautomorphism groupsbirational automorphism groupsFujiki's classfinite bounded subgroupsfree actionsnon-abelian free groupscomplex torus

MSC classification

Primary: 14J50: Automorphisms of surfaces and higher-dimensional varieties
Secondary: 32M05: Complex Lie groups, automorphism groups acting on complex spaces
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 3 , August 2022 , pp. 736 - 746
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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