Équisingularité générique des familles de surfaces à singularité isolée
Equivalences between isolated hypersurface singularities.
Equivariant virtual Betti numbers
We define a generalised Euler characteristic for arc-symmetric sets endowed with a group action. It coincides with the Poincaré series in equivariant homology for compact nonsingular sets, but is different in general. We put emphasis on the particular case of , and give an application to the study of the singularities of Nash function germs via an analog of the motivic zeta function of Denef and Loeser.
Ergänzung zur Arbeit "Quadratische Formen über affinen Algebren und ein algebraischer Beweis des Satzes von Borsuk-Ulam".
Espaces conormaux relatifs. I. Conditions de transversalité
Espaces de Moisezon relatifs et algébrisation des modifications analytiques.
Excess intersection of divisors
Exotische Sphären als Umgebungsränder in speziellen komplexen Räumen.
Explicit birational geometry of threefolds of general type, I
Let be a complex nonsingular projective 3-fold of general type. We prove and for some positive integer . A direct consequence is the birationality of the pluricanonical map for all . Besides, the canonical volume has a universal lower bound .
Explicit computations around the Lichtenbaum-Harshorne vanishing theorem.
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....
Extendability of differential forms on non-isolated singularities.
Extending meromorphic functions on ...m x ...n.
Extension of Morphisms Defined on a Divisor.
Factorization of Birational Morphisms with Fiber Dimension Bounded by 1.
Families of Curves on Surfaces.
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 supersingular abelian surfaces
Fermeture intégrale et changement de base
Fibre de Milnor d'un cône sur une courbe plane singulière.