Complex algebraic variety
From Infogalactic: the planetary knowledge core
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
<templatestyles src="Module:Hatnote/styles.css"></templatestyles>
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.
References
- ↑ Parshin, Alexei N., and Igor Rostislavovich Shafarevich, eds. Algebraic Geometry III: Complex Algebraic Varieties. Algebraic Curves and Their Jacobians. Vol. 3. Springer, 1998.