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
Main article: Chow's theorem

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.

Relation with similar concepts

Not every complex analytic variety is algebraic, though.

gollark: It does get very hot sometimes.
gollark: Hmmmm.
gollark: Good idea.
gollark: Random assignment by bot now, originally not very random assignment by human.
gollark: This seems like a Contingency Gimel-9588 situation, yes.

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