Baum-Bott residue currents

Given a (singular) holomorphic foliation F on a complex manifold, in the 70’s Baum and Bott constructed residue classes associated with the singular components of F. These Baum-Bott residues classes are locally defined (in the sense that they only depend on F close to the singular component) and satisfy an index theorem which computes characteristic classes of F. In the special case when F has rank one and isolated singularities, they can be expressed in terms of the classical Grothendieck residue. I will discuss a joint work with Lucas Kaufmann and Richard Larkang, where we show that the Baum-Bott residue classes of a foliation F are naturally represented by certain residue currents with support on the singular components of F.