Projective algebraic variety: Difference between revisions
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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]]. | 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 field|algebraically closed]]. | |||
==Related notions== | |||
* [[Affine algebraic variety]] | |||
* [[Quasi-affine algebraic variety]] | |||
* [[Quasi-projective algebraic variety]] | |||
* [[Algebraic variety]] | |||
Latest revision as of 16:33, 12 May 2008
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.