Characterization of jacobian Newton polygons of plane branches and new criteria of irreducibility

[Caractérisation des polygones de Newton jacobiens des branches planes et de nouveaux critères d’irréductibilité]

Barroso, Evelia R. García ; Gwoździewicz, Janusz

Annales de l'Institut Fourier, Tome 60 (2010), p. 683-709 / Harvested from Numdam

Résumé

Nous caractérisons de deux manières différentes les polygones de Newton jacobiens des branches planes. Ces caractérisations donnent, en particulier, des critères combinatoires d’irréductibilité des séries complexes en deux variables et des conditions nécessaires pour qu’une courbe dans le plan complexe soit le discriminant d’une branche plane.

Abstract

In this paper we characterize, in two different ways, the Newton polygons which are jacobian Newton polygons of a plane branch. These characterizations give in particular combinatorial criteria of irreducibility for complex series in two variables and necessary conditions which a complex curve has to satisfy in order to be the discriminant of a complex plane branch.

Détail

Publié le : 2010-01-01

MR 2667790 | Zbl 1197.32012

DOI : https://doi.org/10.5802/aif.2536
Classification:  32S55,  14H20
Mots clés: courbe plane irréductible, polygone de Newton jacobien, invariant polaire, racine approchée

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