Equivariant Kaehler models for class $\mathcal{C}$ manifolds

A compact complex manifold belongs to Fujiki’s class $\mathcal{C}$ if it is bimeromorphic to a compact Kaehler manifold. Following a paper by Jia and Meng, I will show how to construct Kaehler bimeromorphic models of class $\mathcal{C}$ manifolds equivariantly with respect to automorphisms preserving a big (1,1)-class. Also I will talk about applications of this result to finite subgroups in the automorphism groups of class $\mathcal{C}$ manifolds.