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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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2014
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| In: |
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales . Serie A, Matemáticas
Year: 2013, Volume: 108, Issue: 1, Pages: 259-279 |
| ISSN: | 1579-1505 |
| DOI: | 10.1007/s13398-013-0139-1 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1007/s13398-013-0139-1
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| Author Notes: | Manuel González Villa |
| Summary: | 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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| Item Description: | Published online: 24 August 2013 Gesehen am 29.10.2020 |
| Physical Description: | Online Resource |
| ISSN: | 1579-1505 |
| DOI: | 10.1007/s13398-013-0139-1 |