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On ν-quasi-ordinary power series: factorization, Newton trees and resultants

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Artal Bartolo, Enrique and Cassou-Noguès, Pierrette and Luengo Velasco, Ignacio and Melle Hernández, Alejandro (2011) On ν-quasi-ordinary power series: factorization, Newton trees and resultants. In Topology of algebraic varieties and singularities. Contemporary Mathematics (538). American Mathematical Society, Providence, pp. 321-343. ISBN 978-0-8218-4890-6

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Abstract

The concept of ν-quasi-ordinary power series, which is a generalization of quasi-ordinary power series, was first introduced by H. Hironaka. In the paper under review, the authors study ν-quasi-ordinary power series and give a factorization theorem for ν-quasi-ordinary power series in the first part. The proof of the theorem uses Newton maps. In the second part of the paper, using the factorization theorem, they introduce the Newton tree to encode the Newton process for any hypersurface singularity defined by a power series germ as in Notation 1.1. Finally, the authors describe a condition for two ν-quasi-ordinary power series to have an "intersection multiplicity " by using Newton trees and they can also compute this generalized intersection multiplicity, resultants and discriminant.


Item Type:Book Section
Additional Information:

Papers from the Conference on Topology of Algebraic Varieties, in honor of Anatoly Libgober's 60th birthday, held in Jaca, June 22–26, 2009

Uncontrolled Keywords:Quasi-ordinary power series, resultant, factorisation
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:20877
Deposited On:16 Apr 2013 16:19
Last Modified:02 Aug 2018 11:30

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