Quotients jacobiens d’applications polynomiales
[Jacobian quotients of polynomial mappings]
Annales de l'Institut Fourier, Volume 53 (2003) no. 2, pp. 399-428.

Let ϕ:=(f,g): 2 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.

Soit ϕ:=(f,g): 2 2 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.

DOI: 10.5802/aif.1948
Classification: 14F45,  57M25
Keywords: polynomial mappings, jacobian quotients, Newton polygon, graph manifolds
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Artal Bartolo, Enrique; Cassou-Noguès, Philippe; Maugendre, Hélène. Quotients jacobiens d’applications polynomiales. Annales de l'Institut Fourier, Volume 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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