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

Volume 58 / 1993

Zbigniew Jelonek 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 $(∏_{i=1}^n deg f_i - μ (f)) / (min_{i=1,...,n} deg f_i)$.

Authors

  • Zbigniew Jelonek

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