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

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 ${\mathcal C}$.