Decomposition of polyharmonic functions with respect to the complex Dunkl Laplacian.
Décompositions dans certaines algèbres de Fréchet de fonctions holomorphes.
Dans ce travail, nous étudions le problème de décomposicion suivant: Étant donnés deux ouverts bornés de Cp, Ω1 et Ω2 (vérifiant certaines conditions) et étant donnée une matrice A(z), carrée d'ordre n, dont les coefficients sont des fonctions holomorphes dans Ω1 ∩ Ω2, ayant une prolongement C∞ à l'adhérence (Ω1 ∩ Ω2), peut-on trouver deux matrices A1(z), A2(z) holomorphes dans Ω1 et Ω2 respectivement et se prolongeant de manière C∞ à (Ω1) et (Ω2) telles que sur Ω1 ∩ Ω2 on aitA = A1A2.
Decompositions of hypersurface singularities oftype
Applications of singularity theory give rise to many questions concerning deformations of singularities. Unfortunately, satisfactory answers are known only for simple singularities and partially for unimodal ones. The aim of this paper is to give some insight into decompositions of multi-modal singularities with unimodal leading part. We investigate the singularities which have modality k - 1 but the quasihomogeneous part of their normal form only depends on one modulus.
Definable stratification satisfying the Whitney property with exponent 1
We prove that for a finite collection of sets definable in an o-minimal structure there exists a compatible definable stratification such that for any stratum the fibers of its projection onto satisfy the Whitney property with exponent 1.
Deformaciones de gérmenes analíticos equivariantes.
Déformation d'une singularité isolée d'hypersurface et polynômes de Bernstein
Deformation kompakter komplexer Mannigfaltigkeiten.
Déformation localisée de surfaces de Riemann.
Let Y be a Riemann surface with compact boundary embedded into a hyperbolic Riemann surface of finite type X. It is proved that the space of deformations D of Y into X is an open subset of the Teichmüller space T(X) of X. Furthermore, D has compact closure if and only if Y is simply connected or isomorphic to a punctured disk, and D= T(X) if and only if the components of X Y are all disks or punctured disks.
Deformation of Complete Intersections with Singularities.
Deformation of holomorphic maps onto Fano manifolds of second and fourth Betti numbers 1
Let be a Fano manifold with different from the projective space such that any two surfaces in have proportional fundamental classes in . Let be a surjective holomorphic map from a projective variety . We show that all deformations of with and fixed, come from automorphisms of . The proof is obtained by studying the geometry of the integral varieties of the multi-valued foliation defined by the variety of minimal rational tangents of .
Deformation of holomorphic maps onto the blow-up of the projective plane
Deformation of polar methods
We study deformations of hypersurfaces with one-dimensional singular loci by two different methods. The first method is by using the Le numbers of a hypersurfaces singularity — this falls under the general heading of a “polar” method. The second method is by studying the number of certain special types of singularities which occur in generic deformations of the original hypersurface. We compare and contrast these two methods, and provide a large number of examples.
Deformation of Submanifolds of Strongly Negatively Curved Manifolds.
Deformation of Varieties Defined by Sections in Homogeneous Vector Bundles.
Deformation rigidity of the rational homogeneous space associated to a long simple root
Deformationen isolierter Kurvensingularitäten mit eingebetteten Komponenten.
Deformationen von isolierten Singularitäten kohärenter analytischer Garben.
Deformationen von Keimen eigentlicher, holomorpher Abbildungen.
Deformationen von Quotientensingularitäten (nach zyklischen Gruppen).
Déformations à nombre de Milnor constant : quelques résultats sur les polynômes de Bernstein