On the Nature of Thin Complements of Complete Kähler Metrics.
On 'Type' Conditions for Generic Real Submanifolds of Cn.
Problèmes de modules pour des équations différentielles non linéaires du premier ordre
Proper intersection multiplicity and regular separation of analytic sets
We consider complex analytic sets with proper intersection. We find their regular separation exponent using basic notions of intersection multiplicity theory.
Quadratic Forms and Holomorphic Foliations on Singular Surfaces.
Relative tangent cone of analytic sets
We give a characterization of the relative tangent cone of an analytic curve and an analytic set with an improper isolated intersection. Moreover, we present an effective computation of the intersection multiplicity of a curve and a set with s-metrization.
Semi-simple Carrousels and the Monodromy
Let be an open neighborhood of the origin in and let be complex analytic. Let be a generic linear form on . If the relative polar curve at the origin is irreducible and the intersection number is prime, then there are severe restrictions on the possible degree cohomology of the Milnor fiber at the origin. We also obtain some interesting, weaker, results when is not prime.
Sheaves on subanalytic sites
Stratification de Whitney et théorème de Bertini-Sard.
Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique
Sur un point de la théorie des fonctions algébriques de deux variables
The membership problem for polynomial ideals in terms of residue currents
We find a relation between the vanishing of a globally defined residue current on and solution of the membership problem with control of the polynomial degrees. Several classical results appear as special cases, such as Max Nöther’s theorem, for which we also obtain a generalization. Furthermore there are some connections to effective versions of the Nullstellensatz. We also provide explicit integral representations of the solutions.
The nilpotent part and distinguished form of resonant vector fields or diffeomorphisms
Zur lokalen Hochschild-Homologie eines komplexen Raums.