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]

The Riemann sphere is one of the simplest complex algebraic varieties.

Chow's theorem

Chow's theorem states that a projective analytic variety; i.e., a closed analytic subvariety of the complex projective space $\mathbb {C} \mathbf {P} ^{n}$ 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.

gollark: ... seriously? I have exactly the same issue?

gollark: Oh. Oh, right.

gollark: Anyway, it seems that due to a minor issue of some sort in my code somewhere, this always produces zero. What joy.

gollark: Belgium doesn't *actually* exist.

gollark: Wow, I sure "fixed" my code.

References

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

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

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