Quotients jacobiens d'applications polynomiales  [ Jacobian quotients of polynomial mappings ]
Annales de l'Institut Fourier, Volume 53 (2003) no. 2, p. 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 : https://doi.org/10.5802/aif.1948
Classification:  14F45,  57M25
Keywords: polynomial mappings, jacobian quotients, Newton polygon, graph manifolds
@article{AIF_2003__53_2_399_0,
     author = {Artal Bartolo, Enrique and Cassou-Nogu\`es, Philippe and Maugendre, H\'el\`ene},
     title = {Quotients jacobiens d'applications polynomiales},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {2},
     year = {2003},
     pages = {399-428},
     doi = {10.5802/aif.1948},
     zbl = {1100.14529},
     mrnumber = {1990002},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2003__53_2_399_0}
}
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. http://www.numdam.org/item/AIF_2003__53_2_399_0/

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