On the holonomy Lie algebra and the nilpotent completion of the fundamental group of the complement of hypersurfaces

Abstract

The purpose of this paper is to establish the following isomorphism of Lie algebras.Main Theorem. Let X be the complement of a hypersurface S in the complex projective space PN. Then the tower of nilpotent complex Lie algebras associated with the fundamental group π1(X, *) and the holonomy Lie algebraattached to S are isomorphic.