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arXiv · 1512.06623

Compact leaves of codimension one holomorphic foliations on projective manifolds

Benoît Claudon·Frank Loray·Jorge Pereira·Frédéric Touzet
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Abstract

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

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Benoît Claudon, Frank Loray, Jorge Pereira, Frédéric Touzet. 2018-08-30. Compact leaves of codimension one holomorphic foliations on projective manifolds. https://arxiv.org/abs/1512.06623

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