A Residue Formula for Meromorphic Connections and Applications to Stable Sets of Foliations

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...

Full description

Saved in:
Bibliographic Details
Published in:The Journal of geometric analysis 2023-10, Vol.33 (10), Article 338
Main Authors: Adachi, Masanori, Biard, Séverine, Brinkschulte, Judith
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Differential Geometry
Dynamical Systems and Ergodic Theory
Existence theorems
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Hyperspaces
Mathematical analysis
Mathematics
Mathematics and Statistics
Nessim Sibony: In Memoriam
Residues
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 non-existence theorem of Levi flat hypersurfaces with transversely affine Levi foliation in compact Kähler surfaces.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01385-9