Complex-analytic variety

In mathematics, specifically complex geometry, a complex-analytic variety is defined locally as the set of common zeros of finitely many analytic functions. It is analogous to the included concept of complex algebraic variety, and every complex manifold is an analytic variety. Since analytic varieties may have singular points, not all analytic varieties are complex manifolds. A further generalization of analytic varieties is provided by the notion of complex analytic space. An analytic variety is also called a (real or complex) analytic set.

See also

• Algebraic variety
• Analytic space
• Complex manifold
• Several complex variables

References

• Chirka, Evgeniǐ Mikhaǐlovich (1989), Complex analytic sets, Mathematics and Its Application (Soviet Series), 46, Dordrecht-Boston-London: Kluwer Academic Publishers, ISBN 0-7923-0234-6, MR 1111477, Zbl 0683.32002 . See chapter 1, paragraph 2 Definition and simplest properties of analytic sets. Sets of codimension 1.
• Whitney, Hassler (1972), Complex analytic varieties, Addison-Wesley Series in Mathematics, Reading-Menlo Park-London-Don Mills: Addison-Wesley, ISBN 0-201-08653-0, MR 0387634, Zbl 0265.32008 . See chapter 2, Analytic varieties.

External links

• "Analytic set". PlanetMath. .
• Chirka, Evgeniǐ Mikhaǐlovich (2001) [1994], "Analytic set", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4 .