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A reduction of the Jacobian Conjecture to the symmetric case
Author(s):
Michiel
de Bondt;
Arno
van den Essen
Journal:
Proc. Amer. Math. Soc.
133
(2005),
2201-2205.
MSC (2000):
Primary 14R15, 14R10
Posted:
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  , where  is homogeneous (of degree 3) and  is nilpotent and symmetric. Also a 6-dimensional counterexample is given to a dependence problem posed by de Bondt and van den Essen (2003).
References:
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- 2.
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- 3.
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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:
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
Posted:
March 4, 2005
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2005,
American Mathematical Society
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