A note on the plane Jacobian conjecture

Abstract

It is shown that every polynomial function $P:{\mathbb{C}}^2⟶\mathbb{C}$ with irreducible fibres of same a genus is a coordinate. In consequence, there does not exist counterexamples F = (P,Q) to the Jacobian conjecture such that all fibres of P are irreducible curves of same a genus.

arXiv comment6 pages, some additional terms