A Moishezon manifold is projective if and only if it is Kähler. This is no longer true for a singular Moishezon space. Moishezon proved projectivity criterion for Moishezon spaces with isolated singularities, and for rational singularities it is Known also.

So this is natural to ask Moishezon space with canonical singularites in the sense of MMP is projective iff it is Kähler?