Plane Jacobian conjecture for simple polynomials

A non-zero constant Jacobian polynomial map F = (P, Q) : C-2 -> C-2 has a polynomial inverse if the component P is a simple polynomial, i.e. its regular extension to a morphism p: X -> P-1 in a compactification X of C-2 has the following property: the restriction of p to each irreducible component C of the compactification divisor D = X-C-2 is of degree 0 or 1.