no. 2
Quotients jacobiens d'applications polynomiales
Artal Bartolo, Enrique1 ; Cassou-Noguès, Philippe2 ; Maugendre, Hélène
1 Universidad de Zaragoza, Departamento de Matemáticas, 50009 Zaragoza (Espagne), Université Bordeaux I, Mathématiques Pures de Bordeaux, 351 cours de la Libération, 33405 Talence Cedex (France)
2 Université Grenoble I, Institut Fourier, UMR 5582 du CNRS, BP 74, 38402 Saint-Martin d'Hères, France
Annales de l'Institut Fourier, Tome 53 (2003) no. 2, pp. 399-428.

Soit φ:=(f,g):ℂ 2 →ℂ 2 où f et g sont des applications polynomiales. Nous établissons le lien qui existe entre le polygone de Newton de la courbe réunion du discriminant et du lieu de non-propreté de φ et la topologie des entrelacs à l’infini des courbes affines f -1 (0) et g -1 (0). Nous en déduisons alors des conséquences liées à la conjecture du jacobien.

Let φ:=(f,g):ℂ 2 →ℂ 2 where f and g are polynomial maps. A relationship is established between the following two objects: on the one hand, the Newton polygon of the union of the discriminant curve of φ and its non-properness locus, and on the other, the topological type of the link at infinity of the affine curves f -1 (0) and g -1 (0). Some consequences related to the Jacobian Conjecture are obtained.

DOI : 10.5802/aif.1948
Classification : 14F45, 57M25
Mot clés : applications polynomiales, quotients jacobiens, polygone de Newton, variétés graphées
Keywords: polynomial mappings, jacobian quotients, Newton polygon, graph manifolds

Artal Bartolo, Enrique 1 ; Cassou-Noguès, Philippe 2 ; Maugendre, Hélène 

1 Universidad de Zaragoza, Departamento de Matemáticas, 50009 Zaragoza (Espagne), Université Bordeaux I, Mathématiques Pures de Bordeaux, 351 cours de la Libération, 33405 Talence Cedex (France)
2 Université Grenoble I, Institut Fourier, UMR 5582 du CNRS, BP 74, 38402 Saint-Martin d'Hères, France 
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Artal Bartolo, Enrique; Cassou-Noguès, Philippe; Maugendre, Hélène. Quotients jacobiens d'applications polynomiales. Annales de l'Institut Fourier, Tome 53 (2003) no. 2, pp. 399-428. doi : 10.5802/aif.1948. https://aif.centre-mersenne.org/articles/10.5802/aif.1948/

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