In algebraic geometry, a divisorial scheme is a scheme admitting an ample family of line bundles, as opposed to an ample line bundle.
It was introduced in (Borelli 1963) (in the case of a variety) as well as in (SGA 6, Exposé II, 2.2.)
The term "divisorial" refers to the fact that "the topology of these varieties is determined by their positive divisors.
[2] A scheme is then said to be divisorial if there exists such an ample family of invertible sheaves.
[3] A divisorial scheme has the resolution property; i.e., a coherent sheaf is a quotient of a vector bundle.