Residues of Holomorphic Foliations Relative to a General Submanifold

Let F be a holomorphic foliation (possibly with singularities)on a non-singular manifold M, and let V be a complex analyticsubset of M. Usual residue theorems along V in the theory ofcomplex foliations require that V be tangent to the foliation(that is, a union of leaves and singular points of V and F);this is the case for instance for the blow-up of a non-dicriticalisolated singularity. In this paper, residue theorems are introducedalong subvarieties that are not necessarily tangent to the foliation,including the blow-up of the dicritical situation. 2000 MathematicsSubject Classification 53C12, 57R20, 55N15.