Leray Residue Form and Intersection Homology

Andrzej Weber

25 pages

We consider a meromorphic form with a first order pole along a hypersurface $K$. We ask when the Leray residue form determines an element in intersection homology of $K$. We concentrate on $K$ with isolated singularities. We find that the mixed Hodge structure on vanishing cycles plays a decisive role. We give various conditions on the singularities of $K$ which guaranties that residues lie in intersection homology. For $\dim K>1$ all simple singularities satisfy these conditions.