English Dictionary

projective variety

noun

(algebraic geometry) A Zariski closed subvariety of a projective space; the zero-locus of a set of homogeneous polynomials that generates a prime ideal.

The projective variety is a fundamental concept in algebraic geometry.

意味（1）

(algebraic geometry) A Zariski closed subvariety of a projective space; the zero-locus of a set of homogeneous polynomials that generates a prime ideal.

Varieties are sometimes called closed sets and some authors call an open subset of a projective variety a quasiprojective variety. The latter term is in an attempt to unify the concept of affine and projective variety.