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arXiv · 2011.03472

A note on the Jacobian Conjecture

Zbigniew Jelonek
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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.

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Zbigniew Jelonek. 2020-11-06. A note on the Jacobian Conjecture. https://arxiv.org/abs/2011.03472

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