Related papers: Rigidity for dicritical germ of foliation in the c…
We introduce the jet schemes of a holomorphic foliation, and thereby prove an alternate characterisation of simple singularities of codimension-$1$ foliations, independent of any normal form. This leads to an equivalent condition for the…
We study groups of germs of complex diffeomorphisms having a property called irreducibility. The notion is motivated by a similar property of the fundamental group of the complement of an irreducible hypersurface in the complex projective…
In this article, we focus on a very special class of foliations with complex leaves whose diffeomorphism type is fixed. They have a unique compact leaf and the noncompact leaves all accumulate onto it. We show that the complex structure…
We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some hypotheses to guarantee the existence of dicritical singularities of these…
We give a classification of absolutely dicritical foliations of cusp type, that is, the germ of singularities of complex foliations in the complex plane topologically equivalent to the singularity given by the level of the meromorphic…
In this article we study deformations of a holomorphic foliation with a generic non-rational first integral in the complex plane. We consider two vanishing cycles in a regular fiber of the first integral with a non-zero self intersection…
In this paper we give complete analytic invariants for germs of holomorphic foliations in $(\mathbb{C}^2,0)$ that become regular after a single blow-up. Some of them describe the holonomy pseudogroup of the germ and are called transverse…
The properties of the processes of deformation of a packing of rigid grains are analysed when the exact distribution of the normal forces at contacts is known. Importance of grain rotation and of counter-rotation of adjacent grains is…
We study analytic deformations and unfoldings of holomorphic foliations in complex projective plane $\mathbb{C}P(2)$. Let $\{\mathcal{F}_t\}_{t \in \mathbb{D}_{\epsilon}}$ be topological trivial (in $\mathbb{C}^2$) analytic deformation of a…
We combine classic stability results for foliations with recent results on deformations of Lie groupoids and Lie algebroids to provide a cohomological characterization for rigidity of compact foliations on compact manifolds.
We study in this paper several properties concerning singularities of foliations in $(\mathbb{C}^3,\mathbf{0})$ that are pull-back of dicritical foliations in $(\mathbb{C}^2,\mathbf{0})$. Particularly, we will investigate the existence of…
In this article, we develop a systematic cohomological framework for the study of the rigidity of nilpotent Lie foliations with respect to solvable deformations. We introduce the deformation complex associated to a pair of Lie algebras…
We give analytic and algebraic conditions under which a deformation of real analytic functions with non-isolated singular locus is a deformation with fibre constancy.
We study groups of germs of complex diffeomorphisms having a property called irreducibility. The notion is motivated by the similar property of the fundamental group of the complement of na irreducible hypersurface in the complex projective…
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…
In this paper we address the issues of absolute continuity for the center foliation (as well as the disintegration on the non-absolute continuous case) and rigidity of volume preserving partially hyperbolic diffeomorphisms isotopic to a…
We consider a perturbation $f$ of a hyperbolic toral automorphism $L$. We study rigidity related to exceptional properties of the strong and weak stable foliations for $f$. If the strong foliation is mapped to the linear one by the…
Radial germs of holomorphic foliations in dimension two have a characteristic property: they are the only singular foliations whose reduction of singularities has no singular points. We also know that they are desingularized by a single…
We consider a class of foliations on the complex projective plane that are determined by a quadratic vector field in a fixed affine neighborhood. Such foliations, as a rule, have an invariant line at infinity. Two foliations with…
In this note, we consider the rigidity of the focal decomposition of closed hyperbolic surfaces. We show that, generically, the focal decomposition of a closed hyperbolic surface does not allow for non-trivial topological deformations,…