The set of points at which a polynomial map is not proper

Abstract

We describe the set of points over which a dominant polynomial map $f=(f_1,...,f_n) : ℂ^n → ℂ^n$ is not a local analytic covering. We show that this set is either empty or it is a uniruled hypersurface of degree bounded by $(∏_{i=1}^n deg f_i - μ (f)) / (