Related papers: On the structure of codimension 1 foliations with …

In this work we consider foliations of compact manifolds whose holonomy pseudo-group is expansive, and analyze their number of compact leaves. Our main result is that in the codimension-one case this number is at most finite, and we give…

The space of holomorphic foliations of codimension one and degree $d\geq 2$ in $\mathbb{P}^n$ ($n\geq 3$) has an irreducible component whose general element can be written as a pullback $F^*\mathcal{F}$, where $\mathcal{F}$ is a general…

This work establishes a structure theorem for compact K\"ahler manifolds with semipositive anticanonical bundle. Up to finite \'etale cover, it is proved that such manifolds split holomorphically and isometrically as a product of Ricci flat…

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 note, we describe the structure of regular foliations with semi-positive anti-canonical bundle on smooth projective varieties.

In this work, we mainly deal with a two-dimensional singular holomorphic distribution $\mathcal{D}$ defined on $M$, in the two situations $M=\mathbb{P}^n$ or $M=(\mathbb{C}^n,0)$, tangent to a one-dimensional foliation $\mathcal{G}$ on $M$,…

We study a class of holomorphic foliations in (C^3,0) that can be desingularized following the same desingularization chain that a certain quasi-ordinary surface. This intends to be a generalization to the dimension three of the cuspodal…

Let $X$ be a compact K\"ahler manifold and let $(L, \varphi)$ be a pseudo-effective line bundle on $X$. We first define a notion of numerical dimension of pseudo-effective line bundles with singular metrics, and then discuss the properties…

We study codimension $q \geq 2$ holomorphic foliations defined in a neighborhood of a point $P$ of a complex manifold that are completely integrable, i.e. with $q$ independent meromorphic first integrals. We show that either $P$ is a…

We call a foliation $\mathcal{F}$ on a compact manifold infinitesimally rigid if its deformation cohomology $H^{1}(\mathcal{F},N\mathcal{F})$ vanishes. This paper studies infinitesimal rigidity for a distinguished class of Riemannian…

We study holomorphic foliations of aribitrary codimension in smooth complete toric varieties. We show that split foliations are stable if some good behaviour of their singular set is provided. As an application of these results, we exhibit…

A classical theorem of Micallef says that if $F \colon (\Sigma, g) \to \mathbb{R}^4$ is a stable minimal immersion of an oriented $2$-dimensional complete Riemannian manifold (that is parabolic) into $\mathbb{R}^4$, it is necessarily…

A noncompact (oriented) surface satisfies the condition $(\star)$ if their isolated ends are ''accumulated by genus''. We show that every surface satisfying this condition is homeomorfic to the leaf of a minimal codimension one foliation on…

Let $X$ be a complex surface and $Y$ be an elliptic curve embedded in $X$. Assume that there exists a non-singular holomorphic foliation $\mathcal{F}$ with $Y$ as a compact leaf, defined on a neighborhood of $Y$ in $X$. We investigate the…

Let $M$ be a smooth algebraic variety of dimension $2(p+q)$ with an algebraic symplectic form and a compatible deformation quantization $\mathcal{O}_h$ of the structure sheaf. Consider a smooth coisotropic subvariety $j: Y \to M$ of…

Given a compact hyperkaehler manifold $M$ and a holomorphic bundle B over $M$, we consider a Hermitian connection $\nabla$ on B which is compatible with all complex structures on $M$ induced by the hyperkaehler structure. Such a connection…

In this work, we consider a specific space of foliations with $C^1$ leaves and H\"older holonomies of the square $M=[0,1]^2$, with some topology and we show that a generic such foliation is non-absolutely continuous, furthermore, the…

We consider singular foliations of codimension one on 3-manifolds, in the sense defined by A. Haefliger as being Gamma_1-structures. We prove that under the obvious linear embedding condition, they are Gamma_1-homotopic to a regular…

For a finite dimensional vector space V of dimension n, we consider the incidence correspondence (or partial flag variety) X in P(V) x P(V*), parametrizing pairs consisting of a point and a hyperplane containing it. We completely…

We review Haefliger's differentiable cohomology for the pseudogroup of diffeomorphisms of $\mathbb{R}^q$. We investigate the structure needed to define such a cohomology, which, remarkably, is related to the so called Cartan distribution…