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

Let X be a compact complex space in Fujiki’s class 𝒞 . In this paper, we show that X admits a compact Kähler model X̃ , that is, there exists a projective bimeromorphic map σX̃→ X from a compact Kähler manifold X̃ such that the automorphism group Aut(X) lifts holomorphically and uniquely to a subgroup of Aut(X̃) . 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 𝒞 .