1 results
Strongly Jordan property and free actions of non-abelian free groups
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 3 / August 2022
- Published online by Cambridge University Press:
- 11 August 2022, pp. 736-746
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- Article
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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.
