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A system of polynomial equations related to the Jacobian Conjecture

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arxiv 1406.0886 v3 pith:BDGP5BOV submitted 2014-06-03 math.AG math.AC

Jorge A. Guccione , Juan José Guccione , Christian Valqui This is my paper
classification math.AGmath.AC
keywords systemconjectureequationsjacobianpolynomialprovesolutionanalyse
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We prove that the Jacobian conjecture is false if and only if there exists a solution to a certain system of polynomial equations. We analyse the solution set of this system. In particular we prove that it is zero dimensional.

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  1. The Groebner basis and solution set of a polynomial system related to the Jacobian conjecture

    math.AG 2025-06 conditional novelty 5.0 of 10

    For the n=3, nu_i=0 case of the Jacobian-related system, the reduced Groebner basis is triangular in C_{-1} and C_{-2}, and the solution set splits into four parametrized cases.

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