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

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.

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

References in corpus (1)

• Diffeomorphism Groups of Compact 4-manifolds are not always Jordan

Cited by in corpus (3)

• Automorphisms of surfaces over fields of positive characteristic
• Automorphism groups of $P^1$-bundles over a non-uniruled base
• Automorphism groups of compact complex surfaces: T-Jordan property, Tits alternative and solvability