Newton process and semigroups of irreducible quasi-ordinary power series

• Verfasst von: González Villa, Manuel [VerfasserIn]
• Titel: Newton process and semigroups of irreducible quasi-ordinary power series
• Verf.angabe: Manuel González Villa
• Jahr: 2014
• Jahr des Originals: 2013
• Umfang: 21 S.
• Fussnoten: Published online: 24 August 2013 ; Gesehen am 29.10.2020
• Titel Quelle: Enthalten in: Real Academia de Ciencias Exactas, Físicas y Naturales (Madrid)Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales / A
• Ort Quelle: Heidelberg [u.a.] : Springer, 2001
• Jahr Quelle: 2014
• Band/Heft Quelle: 108(2014), 1, Seite 259-279
• ISSN Quelle: 1579-1505
• DOI: doi:10.1007/s13398-013-0139-1
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1737352656

Abstract

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.