Invertible polynomial mappings via Newton non-degeneracy

Chen, Ying; Dias, Luis Renato G.; Takeuchi, Kiyoshi; Tibăr, Mihai

doi:10.5802/aif.2897

Invertible polynomial mappings via Newton non-degeneracy
[Applications polynomiales inversibles et non-dégénérescence des polyèdres de Newton]

Chen, Ying ¹ ; Dias, Luis Renato G.¹ ; Takeuchi, Kiyoshi ² ; Tibăr, Mihai ³

¹ Universidade de São Paulo ICMC Av. Trabalhador São-Carlense, 400 CP Box 668, 13560-970 São Carlos São Paulo (Brazil)
² University of Tsukuba Institute of Mathematics 1-1-1, Tennodai, Tsukuba Ibaraki, 305-8571 (Japon)
³ Université Lille 1 Mathématiques, Laboratoire Paul Painlevé 59655 Villeneuve d’Ascq (France)

Annales de l'Institut Fourier, Tome 64 (2014) no. 5, pp. 1807-1822.

Résumé
Abstract

On démontre une condition suffisante pour le problème Jacobien dans le contexte des applications polynomiales réelles, complexes ou mixtes. Ceci résulte de l’étude de l’ensemble de bifurcation d’une application soumise à une nouvelle condition de non-dégénérescence par rapport aux polyèdres de Newton à l’infini.

We prove a sufficient condition for the Jacobian problem in the setting of real, complex and mixed polynomial mappings. This follows from the study of the bifurcation locus of a mapping subject to a new Newton non-degeneracy condition.

MR Zbl | 1 citation dans Numdam

DOI : 10.5802/aif.2897

Classification : 14D06, 58K05, 57R45, 14P10, 32S20, 58K15
Keywords: real and complex polynomial mappings, bifurcation locus, Jacobian problem, Newton polyhedron, regularity at infinity
Mot clés : applications polynomiales réelles ou complexes, ensemble de bifurcation, problème Jacobien, polyèdre de Newton, regularité à l’infini

Affiliations des auteurs :

Chen, Ying ¹ ; Dias, Luis Renato G. ¹ ; Takeuchi, Kiyoshi ² ; Tibăr, Mihai ³

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     title = {Invertible polynomial mappings via {Newton} non-degeneracy},
     journal = {Annales de l'Institut Fourier},
     pages = {1807--1822},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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     url = {http://www.numdam.org/articles/10.5802/aif.2897/}
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Chen, Ying; Dias, Luis Renato G.; Takeuchi, Kiyoshi; Tibăr, Mihai. Invertible polynomial mappings via Newton non-degeneracy. Annales de l'Institut Fourier, Tome 64 (2014) no. 5, pp. 1807-1822. doi : 10.5802/aif.2897. http://www.numdam.org/articles/10.5802/aif.2897/

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