Related papers: Codimension one foliations in positive characteris…
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…
This work explores the space of foliations on projective spaces over algebraically closed fields of positive characteristic, with a particular focus on the codimension one case. It describes how the irreducible components of these spaces…
In this work, we study dominant rational maps preserving singular holomorphic codimension one foliations on projective manifolds and that exhibit non-trivial transverse dynamics.
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…
A way to characterize the space of leaves of a foliation in terms of connections is proposed. A particular example of vertex algebra cohomology of codimension one foliations on complex curves is considered.
In this paper we classify codimension 1 Mukai foliations on complex projective manifolds
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…
We prove an extension criterion for codimension one foliations on projective hypersurfaces based on the degree of the foliation and the degree of the hypersurface, and we ensure, in some instances, an isomorphism between the corresponding…
The purpose of this paper is to study singular holomorphic foliations of arbitrary codimension defined by logarithmic forms on projective spaces.
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…
In this paper we study transversely holomorphic foliations of complex codimension one with some hypothesis on the transverse structure.
We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.
The aim of this paper is to study codimension one foliations on rational homogeneous spaces, with a focus on the moduli space of foliations of low degree on Grassmannians and cominuscule spaces. Using equivariant techniques, we show that…
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…
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…
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 class of codimension one foliations has been recently introduced by imposing a natural compatibility condition with a closed maximally non-degenerate 2-form. In this paper we study for such foliations the information captured by a…
We introduce the notion of positivity for a real basic $(1,1)$ class in basic Bott-Chern cohomology group on foliated manifolds, and study the relationship between this positivity and the negativity of transverse holomorphic sectional…
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.