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

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Title

Authors ¹

Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

We describe the set of points over which a dominant polynomial map

f = (f_{1}, ..., f_{n}) : ℂ^{n} \to 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

\frac{\prod_{i = 1}^{n} d e g f_{i} - μ (f)}{min_{i = 1, ..., n} d e g f_{i}}

.

polynomial mappings, proper mappings, dominant mappings, analytic covering

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