Complex algebraic variety explained

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

C P ^{n} , is an algebraic variety. These are usually simply referred to as projective varieties.

Hironaka's theorem

X' \to X .

Relation with similar concepts

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

See also

• Complete variety
• Complex analytic variety

Bibliography

• Book: Dan Abramovich

. 10.1142/9789813272880_0066 . 1711.09976 . Abramovich . Dan . Dan Abramovich. Proceedings of the International Congress of Mathematicians (ICM 2018) . Resolution of singularities of complex algebraic varieties and their families . 2017 . 523–546 . 978-981-327-287-3 . 119708681 .

• Resolution of Singularities of an Algebraic Variety over a Field of Characteristic Zero: I . 10.2307/1970486 . 1970486 . Hironaka . Heisuke . Heisuke Hironaka. Annals of Mathematics . 1964 . 79 . 1 . 109–203 .

Notes and References

1. [Aleksei Nikolaevich Parshin|Parshin, Alexei N.]