Quasi-projective scheme

A locally closed subscheme of a projective space . In other words, a quasi-projective scheme is an open subscheme of a projective scheme. A scheme over a field is quasi-projective if and only if there exists on an invertible ample sheaf. A generalization of the notion of a "quasi-projective scheme" is that of a quasi-projective morphism, that is, a morphism of schemes that is the composite of an open imbedding and a projective morphism. A scheme that is both quasi-projective and complete is projective.

References

[a1]	R. Hartshorne, "Algebraic geometry" , Springer (1977) pp. 10; 103