Moishezon manifold

Summary

A Moishezon manifold is a compact connected complex manifold with as many independent meromorphic functions as its dimension. In other words, its algebraic dimension equals its dimension. Every projective manifold is Moishezon. Moishezon proved that every Moishezon manifold becomes projective after finitely many blow-ups along smooth centres. He also proved that a Moishezon manifold is projective if and only if it is Kähler. So Moishezon manifolds are the compact complex manifolds closest to algebraic varieties; they are the manifolds that correspond to proper algebraic spaces.