Geometry of the Jelonek set

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