On relations between Jacobians and resultants of polynomials in two variables

Abstract

This paper investigates some of the connections between the zeros of a polynomial vector field F = (f, g): ℂ2 ← ℂ2 and the Jacobian determinant J(f, g) of f and g. As a consequence, sufficient conditions are given for F to have no zeros. In addition, in the case where F has an inverse F−1, it is proven that F−1 is also polynomial.