Plcard-Lefschetz Theory for the Universal Coverings of Complements to Affine Hypersurfaces

Abstract

We study the global monodromy on the middle homology group of the universal coverings of the complements to non-singular affine hypersurfaces which intersect the hyperplane at infinity transversely. This monodromy can be regarded as a deformation of the monodromy on the middle homology group of the affine hypersurfaces. We show that this representation becomes irreducible when the deformation parameter is generic.