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Approximate roots, toric resolutions and deformations of a plane branch

González Pérez, Pedro Daniel (2010) Approximate roots, toric resolutions and deformations of a plane branch. Journal of the Mathematical Society of Japan, 62 (3). pp. 975-1004. ISSN 0025-5645

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Abstract

We analyze the expansions in terms of the approximate roots of a Weierstrass polynomial f is an element of 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.


Item Type:Article
Additional Information:

Correction of a proof in the paper “Approximate roots, toric resolutions and deformations of a plane branch” in: vol 65, pg 773, 2013

Uncontrolled Keywords:Generalized Tschirnhausen transformation; Newton-Puiseux expansion; hypersurface singularities; polar invariants; curves; irreducibility; approximate roots; deformations of a plane curve; equisingularity criterion
Subjects:Sciences > Mathematics > Algebra
ID Code:15948
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