Invertible polynomial mappings via Newton non-degeneracy

Ying Chen (1, 2) , Luis Renato Gonçalves Dias (2, 1) , Kiyoshi Takeuchi (3) , Mihai Tibar (2)

1 ICMC-USP - Instituto de Ciências Mathemàticas e de Computação [São Carlos]
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 Institute of Mathematics, University of Tsukuba

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.

Mots clés: fibrations; bifurcation locus; Newton polyhedron; singularities of real polynomial mappings; regularity at infinity; semi-algebraic Sard type theorem; atypical values

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Ying Chen, Luis Renato Gonçalves Dias, Kiyoshi Takeuchi, Mihai Tibar. Invertible polynomial mappings via Newton non-degeneracy. Annales de l'Institut Fourier, 2014, 64 (5), pp.1807-1822. ⟨10.5802/aif.2897⟩. ⟨hal-00805586⟩