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Reference.org
Divisorial scheme
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<p>In algebraic geometry, a divisorial scheme is a scheme admitting an ample family of line bundles, as opposed to an <a href="/facts/Ample_line_bundle/XRQKvXGD">ample line bundle</a>. In particular, a <a href="/facts/Quasi-projective_variety/rdBMNK0G">quasi-projective variety</a> is a divisorial scheme and the notion is a generalization of "quasi-projective". It was introduced in (Borelli 1963) (in the case of a variety) as well as in (SGA 6, Exposé II, 2.2.) (in the case of a scheme). The term "divisorial" refers to the fact that "the topology of these varieties is determined by their positive divisors." The class of divisorial schemes is quite large: it includes affine schemes, separated regular (noetherian) schemes and subschemes of a divisorial scheme (such as <a href="/facts/Projective_varieties/aB2XdB7B">projective varieties</a>). </p>