Microlocal tempered inverse image and Cauchy problem.
Milnor algebras versus modular germs for unimodal hypersurface singularities.
Milnor fibration at infinity for mixed polynomials
We study the existence of Milnor fibration on a big enough sphere at infinity for a mixed polynomial f: ℝ2n → ℝ2. By using strongly non-degenerate condition, we prove a counterpart of Némethi and Zaharia’s fibration theorem. In particular, we obtain a global version of Oka’s fibration theorem for strongly non-degenerate and convenient mixed polynomials.
Milnor numbers and the topology of polynomial hypersurfaces.
Minimal Characteristic Exponent of the Gauss-Manin Connection of Isolated Singular Point and Newton Polyhedron.
Minimal models of foliated algebraic surfaces
Minimal, rigid foliations by curves on
We prove the existence of minimal and rigid singular holomorphic foliations by curves on the projective space for every dimension and every degree . Precisely, we construct a foliation which is induced by a homogeneous vector field of degree , has a finite singular set and all the regular leaves are dense in the whole of . Moreover, satisfies many additional properties expected from chaotic dynamics and is rigid in the following sense: if is conjugate to another holomorphic foliation...
Minimal surfaces in sub-riemannian manifolds and structure of their singular sets in the case
We study minimal surfaces in sub-riemannian manifolds with sub-riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called horizontal area functional associated with the canonical horizontal area form. We derive the intrinsic equation in the general case and then consider in greater detail -dimensional surfaces in contact manifolds of dimension . We show that in this case minimal surfaces are projections of a special class of -dimensional surfaces...
Minimal surfaces in sub-Riemannian manifolds and structure of their singular sets in the (2,3) case
We study minimal surfaces in sub-Riemannian manifolds with sub-Riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called horizontal area functional associated with the canonical horizontal area form. We derive the intrinsic equation in the general case and then consider in greater detail 2-dimensional surfaces in contact manifolds of dimension 3. We show that in this case minimal surfaces are projections of a special class of 2-dimensional surfaces...
Minimaux des feuilletages algébriques de
Minorations de nombres de Milnor
Mirror symmetry and Arnold's duality.
Mixed Hodge structure of affine hypersurfaces
In this article we give an algorithm which produces a basis of the -th de Rham cohomology of the affine smooth hypersurface compatible with the mixed Hodge structure, where is a polynomial in variables and satisfies a certain regularity condition at infinity (and hence has isolated singularities). As an application we show that the notion of a Hodge cycle in regular fibers of is given in terms of the vanishing of integrals of certain polynomial -forms in over topological -cycles on...
Moderate and formal cohomology associated with constructible sheaves
Modular deformations and space curve singularities.
We investigate different concepts of modular deformations of germs of isolated singularities (infinitesimal, Artinian, formal). An obstruction calculus based on the graded Lie algebra structure of the tangent cohomology for modular dcformations is introduced. As the main result the characterisation of the maximal infinitesimally modular subgerm of the miniversal family as flattening stratum of the relative Tjurina module is extended from ICIS to space curve singularities.
Modules de feuillages holomorphes singuliers: I équisingularité.
Moduli of Germs of Legendrian Curves
We construct the generic component of the moduli space of the germs of Legendrian curves with generic plane projection topologically equivalent to a curve .
Modulus of analytic classification for the generic unfolding of a codimension 1 resonant diffeomorphism or resonant saddle
We consider germs of one-parameter generic families of resonant analytic diffeomorphims and we give a complete modulus of analytic classification by means of the unfolding of the Écalle modulus. We describe the parametric resurgence phenomenon. We apply this to give a complete modulus of orbital analytic classification for the unfolding of a generic resonant saddle of a 2-dimensional vector field by means of the unfolding of its holonomy map. Here again the modulus is an unfolding of the Martinet-Ramis...
Monodromie et pôles du prolongement méromorphe de
Monodromy and topological classification of germs of holomorphic foliations
We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy contains all the relevant dynamical information, in particular the projective holonomy representations whose topological invariance was conjectured in the eighties by Cerveau and Sad and is proved here under mild hypotheses.