  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.
