On Generic Topological Type of Complex Plane Polynomial Mappings

Abstract

Abstract For given natural numbers $d_1,d_2$, let $\Omega _2(d_1,d_2)$ be the set of all polynomial mappings $F=(f,g):\mathbb{C}^2\to \mathbb{C}^2$ such that $\deg f\le d_1$, $\deg g\le d_2$. We describe the generic topological type in $\Omega _2(d_1,d_2)$. In particular, we show how to effectively determine a member of $\Omega _2(d_1,d_2)$ with generic topology.