Analytic variety

Analytic variety

In mathematics, specifically geometry, an analytic variety is defined locally as the set of common solutions of several equations involving analytic functions. It is analogous to the included concept of complex algebraic variety, and any complex manifold is an analytic variety. Since algebraic varieties may have singular points, not all analytic varieties are complex manifolds. An Analytic variety is also called real or complex analytic set.

References

*Harvrefcol
Surname = Whitney
Given = Hassler
Title = Complex analytic varieties
Publisher = Addison-Wesley
Year = 1972
, ISBN 0-2010-8653-0 chapter 2 "Analytic varieties".
*Harvrefcol
Surname = Chirka
Given = Evgeniǐ Mikhaǐlovich
Title = Complex analytic sets
Publisher = Kluwer Academic Publishers
Year = 1989
Edition = 2nd ed.
, ISBN 0-7923-0234-6, chapter 1, paragraph 2 "Definition and simplest properties of analytic sets. Sets of codimension 1".

External links

*Evgeniǐ Mikhaǐlovich Chirka " [http://eom.springer.de/A/a012410.htm Analytic set] ", Springer-Verlag Online Encyclopaedia of Mathematics.
*" [http://planetmath.org/encyclopedia/AnalyticSet.html Analytic set] " Planetmath.org Encyclopedia.


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