Meaning

2 senses
  1. (not comparable)Locally closed with respect to the Zariski topology on projective n-space; isomorphic to such a set.

  2. (not comparable)Comprising an open subscheme of a projective scheme

Origin

From quasi- + projective, the sense being that projective varieties are closed subsets of

From quasi- + projective, the sense being that projective varieties are closed subsets of projective space while quasi-projective varieties are only required to be locally closed, a strictly weaker condition. The second, scheme-theoretic sense generalizes the first.

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