Related papers: Compact leaves of codimension one holomorphic foli…

Let $Y$ be a compact complex manifold embedded in a complex manifold with unitary flat normal bundle. Our interest is in a sort of the linearizability problem of a neighborhood of $Y$. As a higher-codimensional generalization of Ueda's…

We study codimension one holomorphic foliations on complex projective spaces and compact manifolds under the assumption that the foliation has a projective transverse structure in the complement of some invariant codimension one analytic…

We investigate the accumulation to singular points of leaves of codimension one foliations whose normal bundle is ample, with emphasis on the nonexistence of Levi-flat hypersurfaces.

This paper deals with codimension one (may be singular) foliations on compact K\"alher manifolds whose conormal bundle is assumed to be pseudo-effective. Using currents with minimal singularities, we show that one can endow the space of…

We investigate the geometry of codimension one foliations on smooth projective varieties defined over fields of positive characteristic with an eye toward applications to the structure of codimension one holomorphic foliations on projective…

In this work, we study dominant rational maps preserving singular holomorphic codimension one foliations on projective manifolds and that exhibit non-trivial transverse dynamics.

In this paper we study transversely holomorphic foliations of complex codimension one with some hypothesis on the transverse structure.

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…

This paper is devoted to the study of codimension two holomorphic foliations and distributions. We prove the stability of complete intersection of codimension two distributions and foliations in the local case. Converserly we show the…

A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.

The number of singularities, counted with multiplicity, of a generic codimension one holomorphic distribution on a compact toric orbifold is determined. As a consequence, we give the classification of regular distributions on rational…

We investigate the structure of smooth holomorphic foliations with numerically flat tangent bundles on compact K\"ahler manifolds. Extending earlier results on non-uniruled projective manifolds by the second and fourth authors, we show that…

Let $f:M\to M$ be a dynamically coherent partially hyperbolic diffeomorphism whose center foliation has all its leaves compact. We prove that if the unstable bundle of $f$ is one-dimensional, then the volume of center leaves must be bounded…

We formalize the concepts of holomorphic affine and projective structures along the leaves of holomorphic foliations by curves on complex manifolds. We show that many foliations admit such structures, we provide local normal forms for them…

We consider an embedded general complex torus $C_n$ into a complex manifold $M_{n+d}$ with a unitary flat normal bundle $N_C$. We show the existence of (non-singular) holomorphic foliation in a neighborhood of $C$ in $M$ having $C$ as leaf…

We give sufficient conditions for the tautness of a transversely homogenous foliation defined on a compact manifold, by computing its base-like cohomology. As an application, we prove that if the foliation is non-unimodular then either the…

These are lecture notes for a course to be held. They provide a full discussion of certain analytic aspects of the uniformisation theory of (singular) holomorphic foliations by curves on compact Kaehler manifolds, with emphasis on their…

We prove the following theorem for Holomorphic Foliations in compact complex kaehler manifolds: if there is a compact leaf with finite holonomy, then every leaf is compact with finite holonomy. As corollary we reobtain stability theorems…

Let X be a compact complex surface with a real foliation. If all leaves are compact complex curves, the foliation must be holomorphic.

Ueda's theory is a theory on a flatness criterion around a smooth hypersurface of a certain type of topologically trivial holomorphic line bundles. We propose a codimension two analogue of Ueda's theory. As an application, we give a…