Related papers: Stability of Holomorphic Foliations with Split Tan…

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…

In this work, we begin by showing that a holomorphic foliation with singularities is reduced if and only if its normal sheaf is torsion free. In addition, when the codimension of the singular locus is at least two, it is shown that being…

We study codimension one holomorphic distributions on the projective three-space, analyzing the properties of their singular schemes and tangent sheaves. In particular, we provide a classification of codimension one distributions of degree…

In the paper Stability of Holomorphic Foliations with Split Tangent Sheaf one finds a study of the locus $\mathrm{Dec}$ where the tangent sheaf of a {\it family} of foliations in $\mathbb{P}_{\mathbb C}^n$ is {\it decomposable}, i.e. a sum…

We show a stability-type theorem for foliations on projective spaces which arise as pullbacks of foliations with a split tangent sheaf on weighted projective spaces. As a consequence, we will be able to construct many irreducible components…

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 prove that, if $n\geq 3$, a singular foliation $\mathcal{F}$ on $\mathbb P^n$ which can be written as pull-back, where $\mathcal{G}$ is a foliation in $ {\mathbb P^2}$ of degree $d\geq2$ with one or three invariant lines in general…

Let $\omega$ be a differential $q$-form defining a foliation of codimension $q$ in a projective variety. In this article we study the singular locus of $\omega$ in various settings. We relate a certain type of singularities, which we name…

A holomorphic foliation is defined as an integrable coherent subsheaf of the tangent sheaf. The structure of the leaves around a singularity is read off from the structure of the stalks. This was done by Baum when the dimension of the…

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…

Let $\mathcal{F}$ be written as $ f^{*}(\mathcal{G})$, where $\mathcal{G}$ is a $1$-dimensional foliation on $ {\mathbb P^{n-1}}$ and $f:{\mathbb P^n}--->{\mathbb P^{n-1}}$ a non-linear generic rational map. We use local stability results…

Let $\mathcal{F}$ be a singular holomorphic foliation of dimension $k>1$ on a projective $n$-manifold $X$. Assume that the determinant of the normal sheaf of $\mathcal{F}$ is ample (as is always the case when $X=\mathbb{P}^{n}$), and that…

We study the conormal sheaves and singular schemes of 1-dimensional foliations on smooth projective varieties $X$ of dimension 3 and Picard rank 1. We prove that if the singular scheme has dimension 0, then the conormal sheaf is…

We prove a complete classification of degree-$2$ foliations on $\mathbb{P}^n$ in any dimension, assuming they are not algebraically integrable. If $\mathcal{F}$ is such a foliation, then either $\mathcal{F}$ is the linear pull-back of a…

We consider a perturbation $f$ of a hyperbolic toral automorphism $L$. We study rigidity related to exceptional properties of the strong and weak stable foliations for $f$. If the strong foliation is mapped to the linear one by the…

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 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…

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…

Let $\mathcal{F}$ be written as $ f^{*}\mathcal{G}$, where $\mathcal{G}$ is a foliation in $ {\mathbb P^2}$ with three invariant lines in general position, say $(XYZ)=0$, and $f:{\mathbb P^n}--->{\mathbb P^2}$,…

Let $X$ a projective manifold equipped with a codimension $1$ (maybe singular) distribution whose conormal sheaf is assumed to be pseudoeffective. By a theorem of Jean-Pierre Demailly, this distribution is actually integrable and thus…