Plane Jacobian conjecture for simple polynomials

Abstract

A non-zero constant Jacobian polynomial map $F=(P,Q):{\mathbb{C}}^2⟶{\mathbb{C}}^2$ has a polynomial inverse if the component $P$ 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.

arXiv comment6 pages, submitted