Newton process and semigroups of irreducible quasi-ordinary power series

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 descr...

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1. Verfasser: González Villa, Manuel (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 2014
In: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales . Serie A, Matemáticas
Year: 2013, Jahrgang: 108, Heft: 1, Pages: 259-279
ISSN:1579-1505
DOI:10.1007/s13398-013-0139-1
Online-Zugang:Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s13398-013-0139-1
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Verfasserangaben:Manuel González Villa

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520 |a 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. 
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