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