A note on the Jacobian Conjecture

2020/11/06 by Zbigniew Jelonek, Jelonek, Zbigniew
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Control and Dynamics of Mobile Robots #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2011.03472

openalex publication_date 2020/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F:\Bbb Cⁿ→\Bbb Cⁿ be a polynomial mapping with a non vanishing Jacobian. If the set S_F of non-properness of F is smooth, then F is a surjective mapping. Moreover, the set S_F can not be connected (this is the Nollet-Xavier Conjecture). Additionally, if n=2, then the set S_F of non-properness of F cannot be a curve without self-intersections.

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