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

Barroso, Evelia R. García; Gwoździewicz, Janusz

Annales de l'Institut Fourier, Tome 60 (2010) no. 2, pp. 683-709.

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.

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.

Classification : 32S55, 14H20
Keywords: Irreducible plane curve, jacobian Newton polygon, polar invariant, approximate root
Mot clés : courbe plane irréductible, polygone de Newton jacobien, invariant polaire, racine approchée

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