## 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.