Quasi-projective algebraic set

A locally closed affine algebraic set in a projective space, equivalently an open subset of a closed subset of projective space cut out by homogeneous polynomials. Reducibility is allowed for an algebraic set; an irreducible variety with such an embedding is a quasi-projective variety.

An irreducible variety which admits a locally closed embedding into projective space. Open subsets of affine varieties and blowups of algebraic varieties along closed centres give important examples.