Preprint A243/2003
Residues of Holomorphic Foliations Relative to a General Submanifold

Daniel Lehmann | Camacho, César

**Keywords: **
foliations | residues | index theorems.

Let F be a holomorphic foliation (possibly with singularities) on a nonsingular manifold M, and let V be a complex analytic subset of M. Usual residue theorems along V in the theory of complex foliations require that V be tangent to the foliation (i.e. union of leaves and singular
points of V and F): this is the case for instance for the blow-up of a nondicritical isolated singularity. In this paper, we will introduce residue theorems along subvarieties which are not necessarily tangent to the foliation, including the blow-up of the dicritical situation.