Relationship To Affine Varieties
For example, affine space is a Zariski-open subset of projective space, and since any closed affine subset can be expressed as an intersection of the projective completion and the affine space embedded in the projective space, this implies that any affine variety is quasiprojective. There are locally closed subsets of projective space that are not affine, so that quasiprojective is more general than affine. Taking the complement of a single point in projective space of dimension at least 2 gives a non-affine quasiprojective variety. This is also an example of a quasiprojective variety that is neither affine nor projective.
Read more about this topic: Quasiprojective Variety
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