Related papers: Codimension 1 Mukai foliations on complex projecti…
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…
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 study families of singular holomorphic foliations on complex projective manifolds whose total intersection defines a foliation of unexpectedly low codimension.
This paper describes the structure of singular codimension one foliations with numerically trivial canonical bundle on projective manifolds.
We prove that, under mild restrictions, the space of codimension-one foliations of degree one on a smooth projective complete intersection has two irreducible components of logarithmic type. We also prove that the same conclusion holds for…
We classify nonsingular holomorphic foliations of dimension and codimension one on certain Hopf manifolds. More general, we prove that all nonsingular codimension one distributions on intermediary or generic Hopf manifolds are integrable…
We obtain a classification of codimension one holomorphic foliations on $\mathbb P^4$ with degenerate Gauss maps.
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…
We describe the structure of singular transversely affine foliations of codimension one on projective manifolds X with zero first Betti number. Our result can be rephrased as a theorem on rank two reducible flat meromorphic connections.
The aim of this paper is to describe complex foliations on Kahler surfaces.
In this article, we study the geometric properties of codimension one foliations on Riemannian manifolds equipped with vector fields that are closed and conformal. Apart from its singularities, these vector fields define codimension one…
The space of codimension one holomorphic foliations of degree 1 in a projective space has an irreducible component whose general element is a logarithmic differential 1-form with simple poles in three hyperplanes. We compute its projective…
We obtain a local classification of complex homothetic foliations on Kaehler manifolds by complex curves. This is used to construct almost Kaehler, Ricci-flat metrics subject to additional curvature properties.
The purpose of this paper is to study singular holomorphic foliations of arbitrary codimension defined by logarithmic forms on projective spaces.
In this article, we give the structure of codimension one foliations with canonical singularities and numerically trivial canonical class on varieties with klt singularities. Building on recent works of Spicer, Cascini - Spicer and Spicer -…
In this article, we describe the structure of codimension one foliations with canonical singularities and numerically trivial canonical class on varieties with terminal singularities, extending a result of Loray, Pereira and Touzet to this…
We study the space of deformations of a smooth foliation of the 5-sphere by complex manifolds
Irreducible isoparametric foliations of arbitrary codimension q on complex projective spaces CP^n are classified, except if n=15 and q=1. Remarkably, there are noncongruent examples that pull back under the Hopf map to congruent foliations…
We aim to classify codimension 1 foliations $\mathscr{F}$ with canonical singularities and $\nu(K_{\mathscr{F}}) < 3$ on threefolds of general type. We prove a classification result for foliations satisfying these conditions and having…
In this paper we study mildly singular del Pezzo foliations on complex projective manifolds with Picard number one