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arXiv · 2011.09381

Jordan property for automorphism groups of compact spaces in Fujiki's class $C$

Sheng Meng·Fabio Perroni·De-Qi Zhang
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Abstract

Let $X$ be a compact complex space in Fujiki's Class $C$. We show that the group $Aut(X)$ of all biholomorphic automorphisms of $X$ has the Jordan property: there is a (Jordan) constant $J = J(X)$ such that any finite subgroup $G\le Aut(X)$ has an abelian subgroup $H\le G$ with the index $[G:H]\le J$. This extends, with a quite different method, the result of Prokhorov and Shramov for Moishezon threefolds.

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Sheng Meng, Fabio Perroni, De-Qi Zhang. 2020-11-18. Jordan property for automorphism groups of compact spaces in Fujiki's class $C$. https://doi.org/10.1112/topo.12247

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