On the Bifurcation Set of a Polynomial Function and Newton Boundary

Abstract

Let /: C n -*C be a polynomial function. It is well known that there exists a finite set TgC, such that /: C n \f-1 (F^C\r is a locally trivial fibration (see The smallest such set F we call the bifurcation set, denoted by B f (in [1], [2] it is called the set of atypical values). Since the map / is not proper, the set B f contains besides the set J^/ of all critical values of / perhaps some other points (the "critical values at infinity" or "critical values of second type" There are some special cases when the polynomial has no critical values at infinity (hence B f =I f ):Pham [13] and Fedoryuk