Leray Residue for Singular Varieties

Andrzej Weber

10 pages

Suppose M is a complex manifold of dimension n+1 and K is a hypersurface in M. By Poincaré duality we define a residue morphism $res:H^{k+1}(M-K) --> H_{2n-k}(K)$ which generalizes the classical Leray residue morphism to cohomology for smooth K. We are mainly interested in the residues of classes represented by holomorphic n+1-forms on $M-K$ . The purpose of this paper is to show a sequence of local conditions for singularities which allows to lift the homological residue to cohomology or to intersection homology.