On the Existence of Equivariant Kähler Models of Certain Compact Complex Spaces

Abstract

Let \(X\) be a compact complex space in Fujiki’s class \(\mathcal{C}\). In this paper, we show that \(X\) admits a compact Kähler model \({\tilde X}\), that is, there exists a projective bimeromorphic map \(\sigma\colon\tilde{X}\to X\) from a compact Kähler manifold \(\tilde{X}\) such that the automorphism group \(\operatorname{Aut}(X)\) lifts holomorphically and uniquely to a subgroup of \(\operatorname{Aut}({\tilde X})\). As a consequence, we also give a few applications to the Jordan property, the finiteness of torsion groups, and arbitrary large finite abelian subgroups for compact complex spaces in Fujiki’s class \({\mathcal C}\).