A residue formula for meromorphic connections and applications to stable sets of foliations
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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2022
- DOI:
- 10.48550/arXiv.2210.09273
- arXiv:
- arXiv:2210.09273
- Bibcode:
- 2022arXiv221009273A
- Keywords:
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- Mathematics - Complex Variables;
- Mathematics - Dynamical Systems
- E-Print:
- 19 pages. v2: introduction revised and minor inaccuracies corrected