Endliche Automorphismengruppen analytischer C-Algebren und ihre Invarianten.
Equianalytic and equisingular families of curves on surfaces.
Equimultiple Locus of Embedded Algebroid Surfaces and Blowing–up in Characteristic Zero
2000 Mathematics Subject Classification: 14B05, 32S25.The smooth equimultiple locus of embedded algebroid surfaces appears naturally in many resolution processes, both classical and modern. In this paper we explore how it changes by blowing–up.* Supported by FQM 304 and BFM 2000–1523. ** Supported by FQM 218 and BFM 2001–3207.
Equisingular deformations below the Newton boundary
Equisingular deformations of isolated 2-dimensional hyper-surface singularities.
Equisingular generic discriminants and Whitney conditions
The purpose of this article is to show that the Whitney conditions are satisfied for complex analytic families of normal surface singularities for which the generic discriminants are equisingular. According to J. Briançon and J. P. Speder the constancy of the topological type of a family of surface singularities does not imply Whitney conditions in general. We will see here that for a family of minimal normal surface singularities these two equisingularity conditions are equivalent.
Équisingularité générique des familles de surfaces à singularité isolée
Ergänzung und Berichtigung zu : Die Zahl der Spitzen und die Jacobi-Algebra einer isolierten Hyperflächensingularität.
Even sets of nodes on sextic surfaces
We determine the possible even sets of nodes on sextic surfaces in , showing in particular that their cardinalities are exactly the numbers in the set . We also show that all the possible cases admit an explicit description. The methods that we use are an interplay of coding theory and projective geometry on one hand, and of homological and computer algebra on the other. We give a detailed geometric construction for the new case of an even set of 56 nodes, but the ultimate verification of existence...
Exceptional Bundles On Nodal Enriques Surfaces.
Exceptional singular -homology planes
We consider singular -acyclic surfaces with smooth locus of non-general type. We prove that if the singularities are topologically rational then the smooth locus is - or -ruled or the surface is up to isomorphism one of two exceptional surfaces of Kodaira dimension zero. For both exceptional surfaces the Kodaira dimension of the smooth locus is zero and the singular locus consists of a unique point of type and respectively.
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....
Families of Arcs on rational surface singularities.
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...
Fibrations sur le cercle et surfaces complexes
Nous donnons des conditions nécessaires et suffisantes pour qu’une variété de dimension 3 se réalise comme bord d’une famille dégénérée de courbes complexes, et pour qu’un entrelacs dans une 3-variété se réalise comme bord d’un germe de fonction analytique en un point d’une surface complexe normale. Ces résultats s’appuient sur une étude des objets topologiques fournis par de telles fonctions holomorphes : soit une variété de Waldhausen et soit une union finie, éventuellement vide, de fibres...
Fibre de Milnor motivique à l’infini et composition avec un polynôme non dégénéré
Soit un corps de caractéristique nulle, un polynôme de Laurent en variables, à coefficients dans et non dégénéré pour son polyèdre de Newton à l’infini. Soit fonctions non constantes à variables séparées et définies sur des variétés lisses. A la manière de Guibert, Loeser et Merle, dans le cas local, nous calculons dans cet article, la fibre de Milnor motivique à l’infini de la composée en termes du polyèdre de Newton à l’infini de . Pour égal à la somme nous obtenons une formule...
Flache T1-Stabilität in der Stratifizierung Verseller Entfaltungen.
Forme hermitienne canonique sur la cohomologie de la fibre de Milnor d'une hypersurface à singularité isolée.
Function germs defined on isolated hypersurface singularities
Gluing Cohen-Macaulay modules with applications to quasihomogeneous complete intersections with isolated singularities.