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.
Accepted:
DOI: 10.5802/aif.2536
Keywords: Irreducible plane curve, jacobian Newton polygon, polar invariant, approximate root
Keywords: courbe plane irréductible, polygone de Newton jacobien, invariant polaire, racine approchée
García Barroso, Evelia R. 1; Gwoździewicz, Janusz 2
@article{AIF_2010__60_2_683_0, author = {Garc{\'\i}a Barroso, Evelia R. and Gwo\'zdziewicz, Janusz}, title = {Characterization of jacobian {Newton} polygons of plane branches and new criteria of irreducibility}, journal = {Annales de l'Institut Fourier}, pages = {683--709}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {60}, number = {2}, year = {2010}, doi = {10.5802/aif.2536}, mrnumber = {2667790}, zbl = {1197.32012}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2536/} }
TY - JOUR AU - García Barroso, Evelia R. AU - Gwoździewicz, Janusz TI - Characterization of jacobian Newton polygons of plane branches and new criteria of irreducibility JO - Annales de l'Institut Fourier PY - 2010 SP - 683 EP - 709 VL - 60 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2536/ DO - 10.5802/aif.2536 LA - en ID - AIF_2010__60_2_683_0 ER -
%0 Journal Article %A García Barroso, Evelia R. %A Gwoździewicz, Janusz %T Characterization of jacobian Newton polygons of plane branches and new criteria of irreducibility %J Annales de l'Institut Fourier %D 2010 %P 683-709 %V 60 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2536/ %R 10.5802/aif.2536 %G en %F AIF_2010__60_2_683_0
García Barroso, Evelia R.; 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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