Plane Jacobian problem for rational polynomials

This paper is to present a geometrical proof of the plane Jacobian conjecture for rational polynomials by an approach of Newton-Puiseux data and geometry of rational surfaces. The obtained result shows that a polynomial map F = (P, Q) : C −→ C with PxQy − PyQx ≡ const. 6= 0 has a polynomial inverse if the component P is a rational polynomial, i.e. if the generic fiber of P is the 2-dimensional topological sphere with a finite number of punctures.