ON THE TOPOLOGY OF POLYNOMIAL MAPPINGS FROM ℂn TO ℂn-1

We consider a polynomial map from ℂn to ℂn-1 and prove that if there exists a so-called very good projection with respect to the value t0, then this value is an atypical value for the map if and only if the Euler characteristic of the fibers are not constant. We describe some topology of the fibers and prove that there is no extension of the characterization of the atypical value via the Lojasiewicz number as in the case n = 2.