论文标题
关于雅各布猜想的笔记
A note on the Jacobian Conjecture
论文作者
论文摘要
令$ f：\ bbb c^n \ to \ bbb c^n $是一个多项式映射，没有消失的jacobian。如果$ f $的非properness的集合$ s_f $平滑，则$ f $是溢流映射。此外，设置$ s_f $无法连接（这是Nollet-Xavier的猜想）。此外，如果$ n = 2 $，则$ f $的非properness的集合$ s_f $不能是没有自我交流的曲线。
Let $F:\Bbb C^n\to\Bbb C^n$ be a polynomial mapping with a non vanishing Jacobian. If the set $S_F$ of non-properness of $F$ is smooth, then $F$ is a surjective mapping. Moreover, the set $S_F$ can not be connected (this is the Nollet-Xavier Conjecture). Additionally, if $n=2$, then the set $S_F$ of non-properness of $F$ cannot be a curve without self-intersections.
