Related papers: Codimension one foliations in positive characteris…
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…
This is a survey paper dealing with holomorphic G-structures and holomorphic Cartan geometries on compact complex manifolds. Our emphasis is on the foliated case: holomorphic foliations with transverse (branched or generalized) holomorphic…
After gluing foliated complex manifolds, we derive a preparation-like theorem for singularities of codimension one foliations and planar vector fields (in the real or complex setting). Without computation, we retrieve and improve results of…
We classify homogeneous polar foliations of codimension two on irreducible symmetric spaces of noncompact type up to orbit equivalence. Any such foliation is either hyperpolar or the canonical extension of a polar homogeneous foliation on a…
This work concerns the problem of relating characteristic numbers of one-dimensional holomorphic foliations of P^n to those of algebraic varieties invariant by them. More precisely: if M is a connected complex manifold, a one-dimensional…
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…
Geometric structures modeled on rational homogeneous manifolds are studied to characterize rational homogeneous manifolds and to prove their deformation rigidity. To generalize these characterizations and deformation rigidity results to…
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…
Starting from the axiomatic description of meromorphic functions with prescribed analytic properties, we introduce the cosimplicial cohomology of restricted meromorphic functions defined on foliations of smooth complex manifolds. Spaces for…
We review properties of closed meromorphic $1$-forms and of the foliations defined by them. We present and explain classical results from foliation theory, like index theorems, the existence of separatrices, and resolution of singularities…
Explicit formulae describing the genus one characters and modular transformation properties of permutation orbifolds of arbitrary Rational Conformal Field Theories are presented, and their relation to the theory of covering surfaces is…
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…
In this paper we study projective flat deformations of projective spaces. We prove that the singular fibers of projective flat deformations of projective spaces appear either in codimension 1 or over singular points of the base. We also…
We present a variant of the classical Darboux-Jouanolou Theorem. Our main result provides a characterization of foliations which are pull-backs of foliations on surfaces by rational maps. As an application, we provide a structure theorem…
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 a continuation of [G-dS1]. We study foliations of two types on Shimura varieties $S$ in characteristic $p$. The first, which we call "tautological foliations", are defined on Hilbert modular varieties, and lift to…
A foliation on a manifold M can be informally thought of as a partition of M into injectively immersed submanifolds, called leaves. In this thesis we study foliations whose leaves carry some specific geometric structures. The thesis…
It is shown that the characteristic classes of foliations that were defined by Losik and that take values in the de~Rham cohomology of the space of infinite order frames over the leaf space may be mapped to the characteristic classes with…
We study conformal structure and topology of leaves of singular foliations by Riemann surfaces.
Two conjectures relating the Kodaira dimension of a smooth projective variety and existence of number of nowhere vanishing 1-forms on the variety are proposed and verified in dimension 3.