  We discuss residue formulae that localize the first Chern class of a line
bundle to the singular locus of a given holomorphic connection. As an
application, we explain a proof for Brunella's conjecture about exceptional
minimal sets of codimension one holomorphic foliations with ample normal bundle
and for a nonexistence theorem of Levi flat hypersurfaces with transversely
affine Levi foliation in compact K\"ahler surfaces.
