2026-06-08T01:06:01Zhttps://docta.ucm.es/rest/oai/request

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

00925njm 22002777a 4500 dc González Pérez, Pedro Daniel author 2010-07 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. 0025-5645 10.2969/jmsj/06230975 https://hdl.handle.net/20.500.14352/42247 http://projecteuclid.org/euclid.jmsj/1280496827 http://projecteuclid.org Approximate roots, toric resolutions and deformations of a plane branch