Plane Jacobian conjecture for simple polynomials

Nguyen Van Chau¹

¹Institute of Mathematics 18 Hoang Quoc Viet, 10307 Hanoi, Vietnam

Annales Polonici Mathematici, Tome 93 (2008) no. 3, pp. 247-251

Résumé

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 $1$.

Détail

DOI : 10.4064/ap93-3-5

Keywords: non zero constant jacobian polynomial map mathbb rightarrow mathbb has polynomial inverse component simple polynomial its regular extension morphism rightarrow mathbb compactification mathbb has following property restriction each irreducible component compactification divisor x mathbb degree