Английская Википедия:Complex algebraic variety

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Файл:RiemannKugel.svg
The Riemann sphere is one of the simplest complex algebraic varieties.

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

Шаблон:Main article Chow's theorem states that a projective complex analytic variety, i.e., a closed analytic subvariety of the complex projective space <math>\mathbb{C}\mathbf{P}^n</math>, is an algebraic variety. These are usually simply referred to as projective varieties.

Hironaka's theorem

Let Шаблон:Mvar be a complex algebraic variety. Then there is a projective resolution of singularities <math>X' \to X</math>.[2]

Relation with similar concepts

Despite Chow's theorem, not every complex analytic variety is a complex algebraic variety.

See also

References

Шаблон:Reflist

Bibliography

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