A residue formula for meromorphic connections and applications to stable sets of foliations (ADACHI Masanori - Shizuoka University and University of Cologne)

We discuss a proof for Brunella’s conjecture: a codimension one holomorphic
foliation on a compact complex manifold of dimension > 2 has no exceptional minimal set
if its normal bundle is ample. The main idea is the localization of the first Chern class of
the normal bundle of the foliation via a holomorphic connection. Although this localization was
done via that of the first Atiyah class in our previous proof, we shall explain that this can be
shown more directly by a residue formula. If time permits, we also discuss a nonexistence result of
Levi flat hypersurfaces with transversely affine Levi foliation. This talk is based on joint works
with S. Biard and J. Brinkschulte.