Related papers: Transversely Lie holomorphic foliations on project…
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 holomorphic foliations with an affine homogeneous transverse structure. We give a friendly characterization of the case of transversely affine foliations in terms of matrix valued pairs of differential forms. This leads naturally…
The purpose of this paper is to study singular holomorphic foliations of arbitrary codimension defined by logarithmic forms on projective spaces.
In this paper we study transversely holomorphic foliations of complex codimension one with some hypothesis on the transverse structure.
A holomorphic foliation $\mathscr{F}$ on a compact complex manifold $M$ is said to be an $\mathscr{L}$-foliation if there exists an action of a complex Lie group $G$ such that the generic leaf of $\mathscr{F}$ coincides with the generic…
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 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 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…
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…
We introduce the holonomy of a singular leaf $L$ of a singular foliation as a sequence of group morphisms from $\pi_n(L)$ to the $\pi_{n-1}$ of the universal Lie $\infty$-algebroid of the transverse foliation of $L$. We include these…
We compute an $L_\infty$-algebroid structure on a projective resolution of some classes of singular foliations on a vector space $V$ induced by the linear action of some Lie subalgebra of $\mathfrak {gl}(V)$. This $L_\infty$-algebroid…
Let F be a codimension one singular holomorphic foliation on a compact complex manifold M. Assume that there exists a meromorphic vector field X on M generically transversal to F. Then, we prove that F is the meromorphic pull-back of an…
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 associate a Lie $\infty$-algebroid to every resolution of a singular foliation, where we consider a singular foliation as a locally generated $\mathscr{O}$-submodule of vector fields on the underlying manifold closed under Lie bracket.…
We prove that any holomorphic codimension 1 foliation on the complex projective plane has at most one singular point up to the action of an ad-hoc birational self map of the complex projective plane into itself. Consequently, any algebraic…
The modular class of a regular foliation is a cohomological obstruction to the existence of a volume form transverse to the leaves which is invariant under the flow of the vector fields of the foliation. By drawing on the relationship…
In this work, we construct some irreducible components of the space of two-dimensional holomorphic foliations on $\mathbb{P}^n$ associated to some algebraic representations of the affine Lie algebra $\mathfrak{aff}(\mathbb{C})$. We give a…
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…
In this paper, we study holomorphic foliations of degree four on complex projective space $\mathbb{P}^n$, where $n\geq 3$, with a special focus on obtaining a structural theorem for these foliations. Furthermore, for a foliation…
In this article we study polynomial logarithmic $q$-forms on a projective space and characterize those that define singular foliations of codimension $q$. Our main result is the algebraic proof of their infinitesimal stability when $q=2$…