Quotients jacobiens d'applications polynomiales

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

Annales de l'Institut Fourier, Tome 53 (2003), p. 399-428 / Harvested from Numdam

Résumé

Soit $\phi :=(f,g) : {\mathbb {C}}^2\rightarrow {\mathbb {C}}^2$ 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 $\phi $ 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.

Abstract

Let $\phi :=(f,g) :{\mathbb {C}}^2\rightarrow {\mathbb {C}}^2$ 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 $\phi $ 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.

Détail

Publié le : 2003-01-01

MR 1990002 | Zbl 1100.14529

DOI : https://doi.org/10.5802/aif.1948
Classification:  14F45,  57M25
Mots clés: applications polynomiales, quotients jacobiens, polygone de Newton, variétés graphées

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