Residues in intersection homology and Lₚ-cohomology

الأصل · EN

Suppose Mⁿ⁺¹ is a complex manifold and K is a hypersurface with isolated singularities. Let ω be a holomorphic form on M K with the first order pole on K. The Leray residue of such form gives an element in the n-th homology of K which is the Alexander dual to [ω]∈ Hⁿ⁺¹(M K). It always lifts to the intersection homology if 0 does not belong to the spectra of a singular points. We assume that singularities are described by the quasihomogeneous equations in certain coordinate systems. Suppose that oscillation indicators of the singular points are greater then -1. Then we find a metric on KΣ in which the residue form is square integrable (and even Lₚ-integrable for p>2). Applying the isomorphism of Lₚ-cohomology and intersection homology we obtain a particular lift of the residue class in homology to intersection homology.