# Complex algebraic variety

{{ safesubst:#invoke:Unsubst||$N=Unreferenced |date=__DATE__ |$B= {{#invoke:Message box|ambox}} }} In algebraic geometry, a complex algebraic variety is an algebraic variety (in the scheme sense or otherwise) over the field of complex numbers. Chow's theorem states that a projective analytic variety; i.e., a closed analytic subvariety of the complex projective space ${\displaystyle \mathbb {C} \mathbf {P} ^{n}}$ is an algebraic variety; it is usually simply referred to as a projective variety. Not every complex analytic variety is algebraic, though.