Jacobian quotients of polynomial mappings

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

  • [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 (2003)

  • Volume: 53, Issue: 2, page 399-428
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Artal Bartolo, Enrique, Cassou-Noguès, Philippe, and Maugendre, Hélène. "Quotients jacobiens d'applications polynomiales." Annales de l’institut Fourier 53.2 (2003): 399-428. <http://eudml.org/doc/116041>.

@article{ArtalBartolo2003,
abstract = {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.},
affiliation = {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); Université Grenoble I, Institut Fourier, UMR 5582 du CNRS, BP 74, 38402 Saint-Martin d'Hères, France},
author = {Artal Bartolo, Enrique, Cassou-Noguès, Philippe, Maugendre, Hélène},
journal = {Annales de l’institut Fourier},
keywords = {polynomial mappings; jacobian quotients; Newton polygon; graph manifolds},
language = {fre},
number = {2},
pages = {399-428},
publisher = {Association des Annales de l'Institut Fourier},
title = {Quotients jacobiens d'applications polynomiales},
url = {http://eudml.org/doc/116041},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Artal Bartolo, Enrique
AU - Cassou-Noguès, Philippe
AU - Maugendre, Hélène
TI - Quotients jacobiens d'applications polynomiales
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 2
SP - 399
EP - 428
AB - 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.
LA - fre
KW - polynomial mappings; jacobian quotients; Newton polygon; graph manifolds
UR - http://eudml.org/doc/116041
ER -

References

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