Approximate roots, toric resolutions and deformations of a plane branch
Pedro Daniel GONZÁLEZ PÉREZ
Source: J. Math. Soc. Japan Volume 62, Number 3
(2010), 975-1004.
Abstract
We analyze the expansions in terms of the approximate roots of a Weierstrass polynomial f ∈ C {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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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1280496827
Digital Object Identifier: doi:10.2969/jmsj/06230975
Mathematical Reviews number (MathSciNet): MR2648070
Zentralblatt MATH identifier: 05786478
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