The set of points at which a polynomial map is not proper
Volume 58 / 1993
Annales Polonici Mathematici 58 (1993), 259-266
DOI: 10.4064/ap-58-3-259-266
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 $(∏_{i=1}^n deg f_i - μ (f)) / (min_{i=1,...,n} deg f_i)$.
