Newton process and semigroups of irreducible quasi-ordinary power series - González Villa, Manuel (Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales . Serie A, Matemáticas, 2014)
The Newton process were introduced by Artal-Bartolo, Cassou-Noguès, Luengo and Melle-Hernández as a generalization of the Newton algorithm associated to plane curve singularities. Newton process is useful to study ν-quasi-ordinary and quasi-ordinary polynomials in any number of variables. We describe numerically the Newton process associated to a quasi-ordinary branch of an irreducible quasi-ordinary polynomial in terms of its characteristic exponents. We show the relation between these numerical data and the semigroup of the singularity, give a criterium for irreducibility of quasi-ordinary polynomials and describe the normalization of irreducible quasi-ordinary surfaces in terms of the numerical data. We also study why and when irreducibility fails to be preserved by the Newton process.
Published online: 24 August 2013
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