Fujiki class C

Summary

Fujiki class $\mathcal{C}$ is the class of compact complex manifolds that are bimeromorphic to compact Kähler manifolds. It contains all compact Kähler manifolds and all Moishezon manifolds. Unlike the Kähler property, membership in class $\mathcal{C}$ is invariant under bimeromorphic maps and under images of holomorphic maps. Manifolds in class $\mathcal{C}$ keep much of the topology of Kähler manifolds: their cohomology has a Hodge decomposition, and their odd Betti numbers are even.