# Complex algebraic variety

In algebraic geometry, a complex algebraic variety is an algebraic variety (in the scheme sense or otherwise) over the field of complex numbers.[1]

## Chow's theorem

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.

## Relation with similar concepts

Not every complex analytic variety is algebraic, though.

## References

1. Parshin, Alexei N., and Igor Rostislavovich Shafarevich, eds. Algebraic Geometry III: Complex Algebraic Varieties. Algebraic Curves and Their Jacobians. Vol. 3. Springer, 1998.