Determination of baum-bott residues of higher codimensional foliations

Let F be a singular holomorphic foliation, of codimension k, on a complex compact manifold such that its singular set has codimension ≥ k+1. In this work we determinate Baum-Bott residues for F with respect to homogeneous symmetric polynomials of degree k + 1. We drop the Baum-Bott's generic hypothesis and we show that the residues can be expressed in terms of the Grothendieck residue of an one-dimensional foliation on a (k + 1)-dimensional disc transversal to a (k +1)-codimensional component of the singular set of F. Also, we show that Cenkl's algorithm for non-expected dimensional singularities holds dropping the Cenkl's regularity assumption.