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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A reduction of the Jacobian Conjecture to the symmetric case


Authors: Michiel de Bondt and Arno van den Essen
Journal: Proc. Amer. Math. Soc. 133 (2005), 2201-2205
MSC (2000): Primary 14R15, 14R10
Published electronically: March 4, 2005
MathSciNet review: 2138860
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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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Additional Information

Michiel de Bondt
Affiliation: Department of Mathematics, Radboud University of Nijmegen, Postbus 9010, 6500 GL Nijmegen, The Netherlands
Email: debondt@math.kun.nl

Arno van den Essen
Affiliation: Department of Mathematics, Radboud University of Nijmegen, Postbus 9010, 6500 GL Nijmegen, The Netherlands
Email: essen@math.kun.nl

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07570-2
PII: S 0002-9939(05)07570-2
Keywords: Jacobian Conjecture, Hessian Conjecture, dependence problems
Received by editor(s): June 30, 2003
Published electronically: March 4, 2005
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2005 American Mathematical Society