On polynomial submersions of degree 4 and the real Jacobian conjecture in R-2

Author(s)

Braun, Francisco ^[1] ; Orefice-Okamoto, Bruna ^[1]

Affiliation

^[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 443, n. 2, p. 688-706, NOV 15 2016.
• Web of Science Citations: 1

Abstract

We prove the following version of the real Jacobian conjecture: ``Let F = (p, q) : R-2 -> R-2 be a polynomial map with nowhere zero Jacobian determinant. If the degree of p is less than or equal to 4, then F is injective{''}. The approach to prove this result leads to a complete classification, up to affine change of coordinates, of the polynomial submersions of degree 4 in R-2 whose level sets are not all connected. (C) 2016 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 13/14014-3 - Equisingularity of determinantal varieties
• Grantee: Bruna Orefice Okamoto
• Support Opportunities: Regular Research Grants
• FAPESP's process: 14/26149-3 - Injectivity of polynomial maps in the plane
• Grantee: Francisco Braun
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 11/08877-3 - Milnor number, Bruce-Roberts number and determinantal varieties
• Grantee: Bruna Orefice Okamoto
• Support Opportunities: Scholarships in Brazil - Post-Doctoral