Residue Form and Intersection Homology
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.