As I understand it, the Nakai-Moishezon criterion gives conditions for the existence of an ample divisor class on an arbitrary proper scheme, and Kleiman's criterion does the same for arbitrary projective schemes (in fact, more generally for 'quasi-divisorial' schemes, as defined in Kleiman's paper).

Are there similar numerical criteria for other 'nice' classes of spaces? In particular, what about Moishezon manifolds? These are not quite schemes, but on the other hand, they *nearly* are, and they are smooth, so one might hope for a useful result.