A note on the Jacobian Conjecture

Zbigniew Jelonek

A note on the Jacobian Conjecture

Algebraic Geometry 2021-09-09 v6 Complex Variables

Authors: Zbigniew Jelonek

Abstract

Let $F:\Bbb C^n\to\Bbb C^n$ 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.

Keywords

jacobian conjecture mapping theory

Cite

@article{arxiv.2011.03472,
  title  = {A note on the Jacobian Conjecture},
  author = {Zbigniew Jelonek},
  journal= {arXiv preprint arXiv:2011.03472},
  year   = {2021}
}

Comments

Versions 4 and 5 are incorrect. There is an mistake in section 2. Versions 1,2,3 are correct. Sorry!

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