ABSTRACT
Nakai-Moishezon criterion For a ringed space (X,O), we let I denote a coherent sheaf of ideals of O. When X is a k-complete scheme (where k is a field), then for any r-dimensional closed subvariety W of X and any invertible sheaf S we let (Sr · W) denote the intersection number of Sr with O/I. The Nakai-Moishezon criterion states that if (Sr · W) > 0 for any rdimensional closed subvariety W of X, then S is ample.
