Plane Jacobian conjecture for simple polynomials

A non-zero constant Jacobian polynomial map $F=(P,Q):$\mathbb{C}$^2 \longrightarrow $\mathbb{C}$^2$hasapolynomialinverseifthecomponent$P$ is a simple polynomial, i.e. if, when $P$ extended to a morphism $p:X⟶{\mathbb{P}}^1$ of a compactification $X$ of ${\mathbb{C}}^2$, the restriction of $p$ to each irreducible component $C$ of the compactification divisor $D=X-{\mathbb{C}}^2$ is either degree 0 or 1.