A Contribution to Keller's jacobian conjecture

Abstract

In the paper there have been investigated polynomial mappings (P,Q): ℂ² → ℂ² in the aspect of the connection between the structure of the jacobian and the coordinates of the mapping. There have been obtained some informations on coefficients of an expansion of the Newton-Puiseux type of one of the coordinates with respect to the other one. Starting from these informations, a theorem is proved stating that if d denotes the degree of the jacobian of the mapping (P,Q), then each of the coordinates P and Q has at most d + 2 zeros at infinity. There have been obtained some equations connecting the homogeneous components of the polynomials P and Q.