Suppose that is an irreducible complex analytic subset of (complex) dimension 1 where is a domain. Suppose that . Then there exists an analytic (holomorphic) map , where is the unit disc, such that and where is a neighbourhood of in , is one to one, and further is a biholomorphism onto . In fact there exist suitable local coordinates in such that is then given by where , where .
This is sometimes written as
A similar result for arbitrary complex analytic sets with singularities of codimension 1 in higher dimensional spaces under further conditions on the singular set was obtained by Stutz, see Chirka  page 98.
- 1 E. M. Chirka. . Kluwer Academic Publishers, Dordrecht, The Netherlands, 1989.
- 2 Alexandru Dimca. . Vieweg, Braunschweig, Germany, 1987.
|Date of creation||2013-03-22 15:20:32|
|Last modified on||2013-03-22 15:20:32|
|Last modified by||jirka (4157)|
|Synonym||Puiseux series parametrization|
|Synonym||Puiseux series normalization|
|Synonym||Puiseux series parameterization|