Related papers: Feuilletages singuliers de codimension un, Groupo\…
In this article, the Galois groupoid of the first Painlev\'{e} equation is computed. This computation use E. Cartan's classification of structural equations of pseudogroups acting on $C^2$ and the degeneration of the first Painlev\'{e}…
This is a survey concerning the relationship between Lie Groupoids (and their morphisms) and singular foliations in the sense of Sussmann-Stefan (considered from a purely geometrical point of view). We focus on the interaction between the…
We introduce the notion of Galois holomorphic foliation on the complex projective space as that of foliations whose Gauss map is a Galois covering when restricted to an appropriate Zariski open subset. First, we establish general criteria…
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 investigate the geometry of codimension one foliations on smooth projective varieties defined over fields of positive characteristic with an eye toward applications to the structure of codimension one holomorphic foliations on projective…
We study the middle convolution of local systems on the punctured affine line in the setting of singular cohomology and in the setting of \'etale cohomology. We derive a formula to compute the topological monodromy of the middle convolution…
The purpose of this paper is to study singular holomorphic foliations of arbitrary codimension defined by logarithmic forms on projective spaces.
Nous d\'ecrivons les singularit\'es de feuilletages holomorphes dicritiques de petite multiplicit\'e en dimension $3$. En particulier nous relions l'existence de d\'eformations et de d\'eploiements non triviaux \`a des probl\`emes…
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 classify nonsingular holomorphic foliations of dimension and codimension one on certain Hopf manifolds. More general, we prove that all nonsingular codimension one distributions on intermediary or generic Hopf manifolds are integrable…
We outline the construction of the holonomy groupoid of a locally Lie groupoid and the monodromy groupoid of a Lie groupoid. These specialise to the well known holonomy and monodromy groupoids of a foliation, when the groupoid is just an…
The Galois/monodromy group of a family of geometric problems or equations is a subtle invariant that encodes the structure of the solutions. Computing monodromy permutations using numerical algebraic geometry gives information about the…
These lecture notes attempt to invite the reader towards the theory of singular foliations, both smooth and holomorphic. In addition to a systematic review of the foundations, and an attempt to put in order examples and several elementary…
We construct the holonomy groupoid of any singular foliation. In the regular case this groupoid coincides with the usual holonomy groupoid of Winkelnkemper (1983); the same holds in the singular cases of Bigonnet and Pradines (1985) and…
We obtain a classification of codimension one holomorphic foliations on $\mathbb P^4$ with degenerate Gauss maps.
The Galois group of a family of cubic surfaces is the monodromy group of the 27 lines of its generic fibre. We describe a method to compute this group for linear systems of cubic surfaces using certified numerical computations. Applying…
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 study Levi-flat real analytic hypersurfaces with singularities. We prove that the Levi foliation on the regular part of the hypersurface can be holomorphically extended, in a suitable sense, to neighbourhoods of singular points.
We give a new construction of the holonomy and fundamental groupoids of a singular foliation. In contrast with the existing construction of Androulidakis and Skandalis, our method proceeds by taking a quotient of an infinite dimensional…
We prove that a one-dimensional foliation with generic singularities on a projective space, exhibiting a Lie group transverse structure in the complement of some codimension one algebraic subset is logarithmic, i.e., it is the intersection…