A note on polynomial maps having fibers of maximal dimension

Abstract

For any two integers k, n, 2 ≤ k ≤ n, let f : (C * ) n → C k be a generic polynomial map with given Newton polytopes. It is known that points, whose fiber under f has codimension one, form a finite set C1(f ) in C k . For maps f above, we show that C1(f ) is empty if k ≥ 3, we classify all Newton polytopes contributing to C1(f ) = ∅ for k = 2, and we compute |C1(f )|.