Dominique Cerveau

IRREDUCIBLE COMPONENTS OF THE SPACE OF HOLOMORPHIC FOLIATIONS OF DEGREE TWO IN CP(N), N 3

In this paper we will prove that the space of holomorphic fo- liations of codimension 1 and degree 2 in CP(n), n > 3, has six irreducible components.

Irreducible components of the space of foliations associated to the affine Lie algebra

In this paper, we give the explicit construction of certain components of the space of holomorphic foliations of codimension one, in complex projective spaces. These components are associated to some algebraic representations of the affine Lie algebra

Ensembles invariants pour un opérateur de transfert dans ℝd

\mathfrak{aff}(\mathbb{C})

Problèmes de modules pour les formes différentielles singulières dans le plan complexe

. Some of them, the so-called exceptional or Klein–Lie components, are rigid in the sense that all generic foliations in the component are equivalent (Example 1). In particular, we obtain rigid foliations of all degrees. Some generalizations and open problems are given at the end of §1.

Algebraic Reduction Theorem for complex codimension one singular foliations

We give the explicit algebraic form of the closed invariant sets for a transfer operator associated to a dilating matrix in ℝd.ResuméNous explicitons la forme algébrique des fermés invariants pour les opérateurs de transfert associés aux matrices dilatantes dans ℝd

Transformations isotropes des germes de feuilletages holomorphes

ResuméOn considère des équations de Pfaff holomorphes à l’origine de ℂ2, ω=a(x, y)dx +b(x, y)dy. Sous des hypothèses génériques, portant sur le premier jet non nulωv deω, on décrit explicitement l’espace des modules de ω pourv petit. On s’intéresse aussi aux formes rigides et aux problèmes sous-jacents à ce type de question, notemment l’invariance topologique de l’holonomie projective.AbstractWe consider holomorphic Pfaffian equations ω=a(x, y)dx +b(x, y)dy. Under generic assumptions on the first significant jet of ω, we describe the space of moduli for Pfaffian equations of small order. Problems of rigidity and topological invariance of projective holonomy are also studied.

Pinceaux linéaires de feuilletages sur CP (3) et conjecture de Brunella

Let

Formes logarithmiques et feuilletages non dicritiques

M

Complete polynomial vector fields in two complex variables

be a compact complex manifold equipped with

Holomorphic foliations desingularized by punctual blow-ups

n=\dim(M)