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oai:docta.ucm.es:20.500.14352/422472023-08-25T11:31:27Zcom_20.500.14352_14col_20.500.14352_15

Approximate roots, toric resolutions and deformations of a plane branch González Pérez, Pedro Daniel 512.76/.77 512.745.2 Generalized Tschirnhausen transformation Newton-Puiseux expansion hypersurface singularities polar invariants curves irreducibility approximate roots deformations of a plane curve equisingularity criterion Álgebra 1201 Álgebra Correction of a proof in the paper “Approximate roots, toric resolutions and deformations of a plane branch” in: vol 65, pg 773, 2013 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. Ministerio de Educación y Ciencia (MEC) Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T00:14:13Z 2023-06-20T00:14:13Z 2010-07 journal article https://hdl.handle.net/20.500.14352/42247 0025-5645 10.2969/jmsj/06230975 eng MTM2007-6798-C02-02 open access application/pdf Math Soc Japan