nLab Moishezon manifold

Moishezon manifold is a compact complex manifold $M$ such that each irreducible component has a field of meromorphic functions of transcendence degree $dim_{\mathbf{C}}M$.

According to a result of Moishezon, a Moishezon manifold has a structure of projective algebraic variety iff it admits a Kahler structure.

There is a somewhat bigger category of Moishezon spaces which happens to be equivalent to algebraic spaces proper over (the spectrum of) $\mathbf{C}$.

Moishezon variety is a compact complex variety that is bimeromorphic to a projective variety.