On stable polynomial mappings

For given natural numbers $d_1,d_2$ let ${\mathrm{\Omega }}_2(d_1,d_2)$ be the set off 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 say that the mapping $F$ is topologically stable in ${\mathrm{\Omega }}_2(d_1,d_2)$ if for every small deformation $F_t\in \Omega_2(d_1,d_2)$themapping$F_t$istopologicallyequivalenttothemapping$F$. The aim of this paper is to characterize the topologically stable mappings in ${\mathrm{\Omega }}_2(d_1,d_2)$. In particular we show how to effectively determine a member of ${\mathrm{\Omega }}_2(d_1,d_2)$ with generic topology.