Residues for Holomorphic Foliations of Singular Pairs

Abstract

Abstract Let X be a (possibly singular) subvariety of a complex manifold M and Y a subvariety of X. We assume that Y is the intersection locus of X with a submanifold P ⊂ M and that this intersection is generically transversal. For such a pair (X, Y), we prove a generalization of the classical Camacho–Sad residue theorem, in case there exists a holomorphic foliation ℱ of X leaving Y invariant. Also, we compute explicitly the residues at isolated singular points.