Quotients jacobiens d'applications polynomiales

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

Annales de l'Institut Fourier, Tome 53 (2003) no. 2, pp. 399-428.

Soit $\phi :=(f,g):{ℂ}^2\to {ℂ}^2$ 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 $f^{-1}\left(0\right)$ et $g^{-1}\left(0\right)$. Nous en déduisons alors des conséquences liées à la conjecture du jacobien.

Let $\phi :=(f,g):{ℂ}^2\to {ℂ}^2$ 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 $f^{-1}\left(0\right)$ and $g^{-1}\left(0\right)$. Some consequences related to the Jacobian Conjecture are obtained.

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

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