论文标题
在稳定的多项式映射上
On stable polynomial mappings
论文作者
论文摘要
对于给定的自然数$ d_1，d_2 $让$ω________________（d_1，d_2）$是所有多项式映射的设置$ f =（f，g）：\ mathbb {c}^2 \ to \ mathbb {c}^2 $，这样的deg $ f \ f \ le d_1 $ d_1 $，deg d_1 $，deg $ g \ g \ g \ l d_2 $。我们说，如果对于每个小变形$ f_t \ inω_2（d_1，d_2）$，映射$ f $在$ω_2（d_1，d_2）$中是拓扑稳定的（d_1，d_2）$映射$ f_t $在拓扑上等于映射$ f $。本文的目的是表征$ω_2（d_1，d_2）$中拓扑稳定的映射。特别是我们展示了如何有效地确定具有通用拓扑的$ω_2（d_1，d_2）$的成员。
For given natural numbers $d_1,d_2$ let $Ω_2(d_1,d_2)$ 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 $Ω_2(d_1,d_2)$ if for every small deformation $F_t\in Ω_2(d_1,d_2)$ the mapping $F_t$ is topologically equivalent to the mapping $F$. The aim of this paper is to characterize the topologically stable mappings in $Ω_2(d_1,d_2)$. In particular we show how to effectively determine a member of $Ω_2(d_1,d_2)$ with generic topology.
