Geometry of the Jelonek set

Let K be an algebraically closed field of an arbitrary characteristic. In this paper, we show that the Jelonek set of a polynomial generically finite map f:Kn→Km (i.e. the set of points at which the map f is not finite) is a K-uniruled variety of pure dimension n-1 or the empty set. We also give an example that it is not necessarily separably uniruled although the map is separable.