A system of polynomial equations related to the Jacobian Conjecture

TL;DR

This paper establishes an equivalence between the Jacobian Conjecture's falsity and the existence of solutions to a specific polynomial system, analyzing the solution set and proving it is zero-dimensional.

Contribution

It introduces a new polynomial system whose solutions determine the truth of the Jacobian Conjecture and analyzes its solution set structure.

Findings

The solution set of the system is zero-dimensional.

The Jacobian Conjecture is false iff the system has a solution.

The solution set analysis provides insights into the conjecture's structure.

Abstract

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.