Newton diagrams and equivalence of plane curve germs
type: Item
instance of: scholarly article
title: Newton diagrams and equivalence of plane curve germs
zbMATH Open document ID: 1111.32029
author: García Evelia R. Barroso
author: Andrzej Lenarcik
author: Arkadiusz Płoski
published in: Journal of the Mathematical Society of Japan
publication date: 2007-04-02T00:00:00Z
review text: The authors study an equivalence of plane curve germs which is weaker than Zariski's equisingularity. Improving \textit{M. Lejeune-Jalabert} [Thèse d'Etat, Paris VII, Janvier 1973)] and \textit{M. Oka} [Proc. Symp. Pure Math. 40, Part 2, 259--268 (1983; Zbl 0514.14003)] theorems on the stability of the Newton boundary they show that the set of all Newton diagrams of a germ is an invariant of this equivalence. Then they give a complete description of the set of all Newton diagrams of a plane many-branched singularity in terms of some invariants of branches and their orders of contact. The properties of the ultrametric space of plane curve germs play an important part in the paper.
reviewed by: Andrzej Lenarcik
Mathematics Subject Classification ID: 32S55
Mathematics Subject Classification ID: 14H20
zbMATH DE Number: 5139569
zbMATH Keywords: plane curve germ
zbMATH Keywords: Newton diagram
zbMATH Keywords: equivalence of terms
zbMATH Keywords: strong triangle inequality
zbMATH Keywords: quasi-branch
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/1180135501
OpenAlex ID: W2071957040
DOI: 10.2969/JMSJ/1180135501
description: scientific article; zbMATH DE number 5139569