Compact leaves of codimension one holomorphic foliations on projective\n manifolds

2015/12/21 by Benoît Claudon, Frank Loray, Claudon, Benoît +5 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1512.06623

openalex publication_date 2015/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article studies codimension one foliations on projective man-ifolds\nhaving a compact leaf (free of singularities). It explores the interplay\nbetween Ueda theory (order of flatness of the normal bundle) and the holo-nomy\nrepresentation (dynamics of the foliation in the transverse direction). We\naddress in particular the following problems: existence of foliation having as\na leaf a given hypersurface with topologically torsion normal bundle, global\nstructure of foliations having a compact leaf whose holonomy is abelian (resp.\nsolvable), and factorization results.\n

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• Holomorphic foliation associated with a semi-positive class of numerical dimension one

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