Related papers: Transversely projective holomorphic foliations wit…

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 $f:{\mathbb P^n}--->{\mathbb P^2}$,…

We provide a natural generalization to submanifolds of the holographic method used to extract higher-order local invariants of both Riemannian and conformal embeddings, some of which depend on a choice of parallelization of the normal…

We introduce and give normal forms for (one-dimensional) Riccati foliations (vector fields) on $\ov \bc \times \bc P(2)$ and $\ov \bc \times \ov \bc^n$. These are foliations are characterized by transversality with the generic fiber of the…

This article is dedicated to the study of singular codimension $1$ foliations $\mathcal{F}$ on a simplicial complete toric variety $X$ and their pullbacks by dominant rational maps $\varphi:\mathbb{P}^n\dashrightarrow X$. First, we describe…

In this paper we study the problem of analytic extension of germs of holonomy of algebraic foliations. More precisely we prove that for a Riccati foliation associated to a branched projective structure over a finite type surface which is…

In this article, for holomorphic foliations of codimension one at $(\mathbb{C}^{3},0)$, we define the family of second type foliations. This is formed by foliations having, in the reduction process by blow-up maps, only well oriented…

On compact foliated manifolds, we extend the theorem on the existence and uniqueness of solutions to generalized Kazdan-Warner equations. We provide examples of PDEs that we solve, including the transverse Hitchin equation for a diagonal…

Let $X$ be a compact K\"ahler manifold and $\alpha$ be a class in the Dolbeault cohomology class of bidegree $(1, 1)$ on $X$. When the numerical dimension of $\alpha$ is one and $\alpha$ admits at least two smooth semi-positive…

We study the geometry of the leaf closure space of regular and singular Riemannian foliations. We give conditions which assure that this leaf space is a singular symplectic or K\"ahler space.

It is shown that codimension one parabolic foliations of complex manifolds are holomorphic. This is proved using the fact that codimension one foliations of complex manifolds are necessarily locally Monge-Amp\`ere foliations and that…

We give a bounding of degree of quasi-smooth hypersurfaces which are invariant by a one dimensional holomorphic foliation of a given degree on a weighted projective space.

This is a survey of the theory of complex projective (CP^1) structures on compact surfaces. After some preliminary discussion and definitions, we concentrate on three main topics: (1) Using the Schwarzian derivative to parameterize the…

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…

We introduce the notion of equivariant basic cohomology for singular Riemannian foliations with transverse infinitesimal actions, and prove some elementary properties such as its invariance under homotopies. For the particular case of…

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…

This work deals with the topological classification of germs of singular foliations on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and…

We prove the following result that was conjectured by Brunella: Let $X$ be a compact complex manifold of dimension $\geq 3$. Let $\mathcal{F}$ be a codimension one holomorphic foliation on $X$ with ample normal bundle. Then every leaf of…

In the main result of this paper we prove that a codimension one foliation of $\mathbb{P}^n$, which is locally a product near every point of some codimension two component of the singular set, has a Kupka component. In particular, we obtain…

We study the singular set of a codimension one holomorphic foliations on $\mathbb{P}^3$. We find a local normal form of a codimension two component of the singular set that is not of Kupka type. We also determined the number of non-Kupka…

We prove that a holomorphic projective connection on a complex projective threefold is either flat, or it is a translation invariant holomorphic projective connection on an abelian threefold. In the second case, a generic translation…