Plane Jacobian conjecture for simple polynomials
Volume 93 / 2008
Annales Polonici Mathematici 93 (2008), 247-251
MSC: Primary 14R15.
DOI: 10.4064/ap93-3-5
Abstract
A non-zero constant Jacobian polynomial map $F=(P,Q):\mathbb{C}^2 \rightarrow \mathbb{C}^2$ has a polynomial inverse if the component $P$ is a simple polynomial, i.e. its regular extension to a morphism $p:X\rightarrow \mathbb{P}^1$ in a compactification $X$ of $\mathbb{C}^2$ has the following property: the restriction of $p$ to each irreducible component $C$ of the compactification divisor $D = X-\mathbb{C}^2$ is of degree $0$ or $1$.
