Espaces conormaux relatifs. I. Conditions de transversalité
Estimation of Lojasiewicz Exponents and Newton Polygons.
Étude du comportement du polynôme de Bernstein lors d’une déformation à constant de avec
Examples of string-theoretic Euler numbers.
Explicit bounds for the Łojasiewicz exponent in the gradient inequality for polynomials
Let f: ℝⁿ → ℝ be a polynomial function of degree d with f(0) = 0 and ∇f(0) = 0. Łojasiewicz’s gradient inequality states that there exist C > 0 and ϱ ∈ (0,1) such that in a neighbourhood of the origin. We prove that the smallest such exponent ϱ is not greater than with .
Explicit models for perserse sheaves.
We consider categories of generalized perverse sheaves, with relaxed constructibility conditions, by means of the process of gluing t-structures and we exhibit explicit abelian categories defined in terms of standard sheaves categories which are equivalent to the former ones. In particular , we are able to realize perverse sheaves categories as non full abelian subcategories of the usual bounded complexes of sheaves categories. Our methods use induction on perversities. In this paper, we restrict...
Explicit resolutions of double point singularities of surfaces.
Locally analytically, any isolated double point occurs as a double cover of a smooth surface. It can be desingularized explicitly via the canonical resolution, as it is very well-known. In this paper we explicitly compute the fundamental cycle of both the canonical and minimal resolution of a double point singularity and we classify those for which the fundamental cycle differs from the fiber cycle. Moreover we compute the conditions that a double point singularity imposes to pluricanonical systems....
Exponents and Newton Polyhedra of Isolated Hypersurface Singularities.
Extendability of differential forms on non-isolated singularities.
Faisceaux pervers dont le support singulier est une courbe plane
Familien komplexer Räume mit streng pseudokonvexer spezieller Faser
Families of Curves on Surfaces.
Families of differential forms on complex spaces
On every reduced complex space we construct a family of complexes of soft sheaves ; each of them is a resolution of the constant sheaf and induces the ordinary De Rham complex of differential forms on a dense open analytic subset of . The construction is functorial (in a suitable sense). Moreover each of the above complexes can fully describe the mixed Hodge structure of Deligne on a compact algebraic variety.
Families of polynomials with total Milnor number constant.
Families of smooth curves on surface singularities and wedges
Following the study of the arc structure of singularities, initiated by J. Nash, we give criteria for the existence of smooth curves on a surface singularity (S,O) and of smooth branches of its generic hypersurface section. The main applications are the following: the existence of a natural partition of the set of smooth curves on (S,O) into families, a description of each of them by means of chains of infinitely near points and their associated maximal cycle and the existence of smooth curves on...
Families of varieties with prescribed singularities
Feuilletages de : de l’holonomie hyperbolique pour les minimaux exceptionnels
Feuilletages holomorphes de codimension un sur les espaces homogènes complexes
Feuilletages holomorphes singuliers sur les surfaces contenant une coquille sphérique globale
En résumé, on retiendra que seules les surfaces d’Inoue-Hirzebruch et les surfaces génériques admettent un feuilletage holomorphe. Sur les surfaces d’Inoue-Hirzebruch il existe exactement deux feuilletages et sur les surfaces génériques au plus un. Le lieu singulier de la réunion des courbes rationnelles coïncide avec le lieu singulier du feuilletage. Les courbes rationnelles sont des feuilles en dehors des points singuliers du feuilletage.
Feuilletages holomorphes singuliers sur les surfaces contenant une coquille sphérique globale