Characterization of jacobian Newton polygons of plane branches and new criteria of irreducibility
Annales de l'Institut Fourier, Volume 60 (2010) no. 2, pp. 683-709.

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.

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.

DOI: 10.5802/aif.2536
Classification: 32S55,  14H20
Keywords: Irreducible plane curve, jacobian Newton polygon, polar invariant, approximate root
Barroso, Evelia R. García 1; Gwoździewicz, Janusz 2

1 Universidad de La Laguna Facultad de Matemáticas Departamento de Matemática Fundamental 38271 La Laguna, Tenerife (Espagne)
2 Technical University Department of Mathematics 25-314 Kielce (Pologne)
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Barroso, Evelia R. García; Gwoździewicz, Janusz. Characterization of jacobian Newton polygons of plane branches  and new criteria of irreducibility. Annales de l'Institut Fourier, Volume 60 (2010) no. 2, pp. 683-709. doi : 10.5802/aif.2536. https://aif.centre-mersenne.org/articles/10.5802/aif.2536/

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