In algebraic geometry, a complex algebraic variety is an algebraic variety (in the scheme sense or otherwise) over the field of complex numbers.Parshin, Alexei N., and Igor Rostislavovich Shafarevich, eds. Algebraic Geometry III: Complex Algebraic Varieties. Algebraic Curves and Their Jacobians. Vol. 3. Springer, 1998.
Chow's theorem
Chow's theorem states that a projective complex analytic variety, i.e., a closed analytic subvariety of the complex projective space , is an algebraic variety. These are usually simply referred to as projective varieties.
Hironaka's theorem Let be a complex algebraic variety. Then there is a projective resolution of singularities .
Relation with similar concepts Despite Chow's theorem, not every complex analytic variety is a complex algebraic variety.
See also Complete variety Complex analytic variety
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