On singular varieties associated to a polynomial mapping from ℂ n to ℂ n-1

Abstract

We construct singular varieties V G associated to a polynomial mapping G: ℂ n → ℂ n-1 where n ≥ 2. Let G: ℂ 3 → ℂ 2 be a local submersion, we prove that if the homology or the intersection homology with total perversity (with compact supports or closed supports) in dimension two of any variety V G is trivial then G is a fibration. In the case of a local submersion G: ℂ n ñ ℂ n-1 where n ≥ 4, the result is still true with an additional condition.