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: I thought executable formats were quite complex. Is HTML powerful enough?

gollark: A HTML... linker?

gollark: 35 minutes remain.

gollark: https://www.notebookcheck.net/NFT-hype-train-makes-it-way-to-Samsung-TVs-allowing-you-to-see-and-purchase-artwork-from-your-living-room.589604.0.html

gollark: Did you know? It is now less practical to escape.

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.