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July, 2010 Approximate roots, toric resolutions and deformations of a plane branch
Pedro Daniel GONZÁLEZ PÉREZ
J. Math. Soc. Japan 62(3): 975-1004 (July, 2010). DOI: 10.2969/jmsj/06230975

Abstract

We analyze the expansions in terms of the approximate roots of a Weierstrass polynomial fC {x}[y], defining a plane branch (C,0), in the light of the toric embedded resolution of the branch. This leads to the definition of a class of (non-equisingular) deformations of a plane branch (C,0) supported on certain monomials in the approximate roots of f, which are essential in the study of Harnack smoothings of real plane branches by Risler and the author. Our results provide also a geometrical approach to Abhyankar's irreducibility criterion for power series in two variables and also a criterion to determine if a family of plane curves is equisingular to a plane branch.

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Pedro Daniel GONZÁLEZ PÉREZ. "Approximate roots, toric resolutions and deformations of a plane branch." J. Math. Soc. Japan 62 (3) 975 - 1004, July, 2010. https://doi.org/10.2969/jmsj/06230975

Information

Published: July, 2010
First available in Project Euclid: 30 July 2010

zbMATH: 1258.14039
MathSciNet: MR2648070
Digital Object Identifier: 10.2969/jmsj/06230975

Subjects:
Primary: 14J17
Secondary: 14M25, 32S10

Rights: Copyright © 2010 Mathematical Society of Japan

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Vol.62 • No. 3 • July, 2010
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