no. 5
Invertible polynomial mappings via Newton non-degeneracy
[Applications polynomiales inversibles et non-dégénérescence des polyèdres de Newton]
Chen, Ying1 ; Dias, Luis Renato G.1 ; Takeuchi, Kiyoshi2 ; Tibăr, Mihai3
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.

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.

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

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) 
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     title = {Invertible polynomial mappings via {Newton} non-degeneracy},
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2897/

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