Related papers: Hypersurfaces quasi-invariant by codimension one f…
We prove a Darboux-Jouanolou type theorem on the algebraic integrability of polynomial differential $r$-forms over arbitrary fields ($r\geq 1$). We also investigate the Darboux's method for producing integrating factors.
We apply ideas related to the strength of polynomials to provide new cases of unirational hypersurfaces. It is famously known that hypersurfaces that are smooth in very high codimension are unirational, and a simple corollary then implies…
In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…
We present a new list of irreducible components of the space of codimension two holomorphic foliations on $\mathbb P^{4}$. They are associated to the pull-back by branched rational maps of 1-dimensional foliations on $\mathbb P^3$ leaving…
The Separatrix Theorem of C. Camacho and P. Sad guarantees the existence of invariant curve (separatrix) passing through the singularity of germ of holomorphic foliation on complex surface, when the surface underlying the foliation is…
We introduce a notion of normal form for transversely projective structures of singular foliations on complex manifolds. Our first main result says that this normal form exists and is unique when ambient space is two-dimensional. From this…
We present a new link between the Invariant Theory of infinitesimal singular Riemannian foliations and Jordan algebras. This, together with an inhomogeneous version of Weyl's First Fundamental Theorems, provides a characterization of the…
Several papers have been written studying unexpected hypersurfaces. We say a finite set of points Z admits unexpected hypersurfaces if a general union of fat linear subspaces imposes less that the expected number of conditions on the ideal…
In this note we study several aspects of coisotropic submanifolds of a contact manifold. In particular we give a structure theorem for the singularity of the characteristic foliation of a coisotropic submanifold. Moreover we establish 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…
The main purpose of this paper is to provide a structure theorem for codimension one singular transversely projective foliationson projective manifolds. To reach our goal, we firstly extend Corlette-Simpson's classification of rank two…
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…
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…
We will use flat divisors, and canonically associated singular holomorphic foliations, to investigate some of the geometry of compact complex manifolds. The paper is mainly concerned with three distinct problems: the existence of…
I give a theory of Moebius-flat hypersurfaces in n-dimensional projective space, analogous to that in conformal geometry. This unifies the classes of hypersurfaces with flat induced conformal structure (n > 3) and a classically studied…
Let $\cal{F}$ be a regular codimension 1 holomorphic foliation on a compact K\" ahler manifold. One assumes in addition that $\cal{F}$ possesses a transverse invariant positive current. The aim of this paper is to establish the following…
This note provides an alternative proof of a result of Labourie. We show that the two complements of the convex core of a three dimensional quasi-fuchsian hyperbolic manifold may be foliated by embedded hypersurfaces of constant Gaussian…
Transverse one dimensional foliations play an important role in the study of codimension one foliations. In \cite{KR2}, the authors introduced the notion of flow box decomposition of a 3-manifold $M$. This is a decomposition of $M$ that…
We study surfaces with one constant principal curvature in Riemannian and Lorentzian three-dimensional space forms. Away from umbilic points they are characterized as one-parameter foliations by curves of constant curvature, each of these…
We study the existence and regularity of invariant graphs for bundle maps (or bundle correspondences with generating bundle maps motivated by ill-posed differential equations) having some relative partial hyperbolicity on non-trivial and…