Projective algebraic variety

Definition
A projective algebraic variety (or simply projective variety) is an irreducible closed subset of the projective space over a field, equipped with the Zariski topology.

We often assume that the underlying field is algebraically closed.

Related notions

 * Affine algebraic variety
 * Quasi-affine algebraic variety
 * Quasi-projective algebraic variety
 * Algebraic variety