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

Sheng Meng; Fabio Perroni; De-Qi Zhang

doi:10.1112/topo.12247

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

Algebraic Geometry 2023-07-06 v3 Group Theory

Authors: 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.

Keywords

jordan property automorphism groups compact complex spaces fujiki class c moishezon threefolds abelian subgroups

Cite

@article{arxiv.2011.09381,
  title  = {Jordan property for automorphism groups of compact spaces in Fujiki's class $C$},
  author = {Sheng Meng and Fabio Perroni and De-Qi Zhang},
  journal= {arXiv preprint arXiv:2011.09381},
  year   = {2023}
}

Comments

This version 3 changed the letter "C" only in the title to be properly displayed; no other change

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

Abstract

Keywords

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