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

Zbigniew Jelonek (1993)

Annales Polonici Mathematici

We describe the set of points over which a dominant polynomial map f = ( f 1 , . . . , f n ) : n 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 d e g f i - μ ( f ) ) / ( m i n i = 1 , . . . , n d e g f i ) .

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