Éclatements quasi homogènes
Ein Torelli-Satz für die unimodalen und bimodularen Hyperflächensingularitäten.
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 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.
Examples of string-theoretic Euler numbers.
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....