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Puiseux parametric equations of analytic sets


Author: Fuensanta Aroca
Journal: Proc. Amer. Math. Soc. 132 (2004), 3035-3045
MSC (2000): Primary 32S05, 32B10; Secondary 14M25
DOI: https://doi.org/10.1090/S0002-9939-04-07337-X
Published electronically: June 2, 2004
MathSciNet review: 2063125
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Abstract: We prove the existence of local Puiseux-type parameterizations of complex analytic sets via Laurent series convergent on wedges. We describe the wedges in terms of the Newton polyhedron of a function vanishing on the discriminant locus of a projection. The existence of a local parameterization of quasi-ordinary singularities of complex analytic sets of any codimension will come as a consequence of our main result.


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Additional Information

Fuensanta Aroca
Affiliation: Instituto de Matematicas UNAM (Unidad Cuernavaca), Apartado Postal 273-3, Administración de Correos 3, CP 62251, Cuernavaca, Morelos, Mexico
Address at time of publication: Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, 13560-970 São Carlos SP, Brazil
Email: fuen@matcuer.unam.mx, fuen@icmc.usp.br

DOI: https://doi.org/10.1090/S0002-9939-04-07337-X
Keywords: Parameterization, wedges, quasi-ordinary singularities
Received by editor(s): February 6, 2002
Received by editor(s) in revised form: May 19, 2003
Published electronically: June 2, 2004
Additional Notes: The author was supported first by Post-doctoral Grant of TMR Project Singularidades de Ecuaciones Diferenciales y Foliaciones at the University of Lisbon, and then by UNAM at Instituto de Matemáticas-Cuernavaca (Mexico)
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2004 American Mathematical Society

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