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PROJECTIVELY FLAT FOLIATIONS

Part of: Complex dynamical systems Birational geometry Local differential geometry Complex manifolds

Published online by Cambridge University Press:  18 March 2025

Stéphane Druel Open the ORCID record for Stéphane Druel [Opens in a new window]
Stéphane Druel*
Affiliation:
CNRS, Université Claude Bernard Lyon 1, UMR 5208, Institut Camille Jordan, F-69622 Villeurbanne, France
*
stephane.druel@math.cnrs.fr
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Abstract

We describe the structure of regular codimension $1$ foliations with numerically projectively flat tangent bundle on complex projective manifolds of dimension at least $4$. Along the way, we prove that either the normal bundle of a regular codimension $1$ foliation is pseudo-effective, or its conormal bundle is nef.

Keywords

Holomorphic foliationsBogomolov-Gieseker inequalityprojective flatness

MSC classification

Primary: 37F75: Holomorphic foliations and vector fields 32Q30: Uniformization 32Q26: Notions of stability
Secondary: 14E20: Coverings 14E30: Minimal model program (Mori theory, extremal rays) 53B10: Projective connections
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 24 , Issue 3 , May 2025 , pp. 763 - 812
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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