Residues of singular holomorphic distributions

Abstract

We present two types of residue theories for singular holomorphic distributions. The first one is for certain Chern polynomials of the normal sheaf of a distribution and the residues arise from the vanishing, by rank reason, of the relevant characteristic classes on the non-singular part. The second one is for certain Atiyah polynomials of vector bundles admitting an action of a distribution and the residues arise from the Bott type vanishing theorem on the non-singular part.