A residue formula for meromorphic connections and applications to stable sets of foliations
arXiv:2210.09273 · doi:10.1007/s12220-023-01385-9
Abstract
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 Kähler surfaces.
19 pages. v2: introduction revised and minor inaccuracies corrected