A note on the Jacobian Conjecture

Zbigniew Jelonek Colloquium Mathematicum MSC: Primary 14R15. DOI: 10.4064/cm8671-12-2021 Published online: 25 April 2022

Abstract

Let $F:\mathbb C^n\to \mathbb C^n$ be a polynomial mapping with non-vanishing Jacobian. If the set $S_F$ of non-properness of $F$ is smooth, then $F$ is a surjective mapping. Moreover, if $S_F$ is connected, then $\chi (S_F) \gt 0.$ Additionally, if $n=2$, then $S_F$ cannot be a curve without self-intersections.

Authors

  • Zbigniew JelonekInstytut Matematyczny PAN
    Śniadeckich 8
    00-656 Warszawa, Poland
    e-mail

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