# Complex algebraic variety

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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 is an algebraic variety; it is usually simply referred to as a projective variety. Not every complex analytic variety is algebraic, though.