A reduction of the Jacobian Conjecture to the symmetric case

de Bondt, Michiel; van den Essen, Arno

doi:10.1090/S0002-9939-05-07570-2

A reduction of the Jacobian Conjecture to the symmetric case
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by Michiel de Bondt and Arno van den Essen

Proc. Amer. Math. Soc. 133 (2005), 2201-2205

DOI: https://doi.org/10.1090/S0002-9939-05-07570-2

Published electronically: March 4, 2005

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Abstract:

The main result of this paper asserts that it suffices to prove the Jacobian Conjecture for all polynomial maps of the form $x+H$, where $H$ is homogeneous (of degree 3) and $JH$ is nilpotent and symmetric. Also a 6-dimensional counterexample is given to a dependence problem posed by de Bondt and van den Essen (2003).

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