ON THE BIFURCATION SET OF COMPLEX POLYNOMIAL WITH ISOLATED SINGULARITIES AT INFINITY

Let f be a complex polynomial. In this paper we give complete descript ions of the bifurcation set of f, provided f has only isolated singula rities at infinity. In particular, we generalize to such polynomials t he Ha-Le Theorem and show that if the Euler characteristic of the fibr es of f is constant over U subset of C, where U contains only regular values of f, then f is actually locally C-infinity-trivial over U. The proof is based on a criterion which allows us to show for some famili es of isolated hypersurface singularities that mu-constant implies top ological triviality.