Determination of Baum-Bott residues of higher codimensional foliations

Abstract

Let $\mathcal{F}$ be a singular holomorphic foliation, of codimension $k$, on a complex compact manifold such that its singular set has codimension $\ge k+1$. In this work we determinate Baum-Bott residues for $\mathcal{F}$ 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 $\mathcal{F}$. Also, we show that Cenkl's algorithm for non-expected dimensional singularities holds dropping the Cenkl's regularity assumption.

13 pages. Improved exposition. To appear in Asian Journal of Mathematics