2006/12/07 by Javier Fernández de Bobadilla, de Bobadilla, Javier Fernandez, María Pe Pereira +1
Mathematics · #32S25 #32S50 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Complex Variables (math.CV) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.math/0612201
openalex publication_date 2006/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We look at topological equisingularity of a holomorphic family of reduced mapping germs ft:(C3,O)->C over a contractible base T having non-isolated singularities, by means of their normalisations. We introduce the notion of Equisingularity at the Normalisation for a family ft and prove that, in many cases, it characterises topological embedded equisingularity and R-equisingularity. Moreover we apply our results to the study of topological A-equisingularity of parametrised surfaces, and in many cases characterise it in terms of the constancy of the Milnor number of the inverse image of the singular sets of the parametrised surfaces. A novelty of our approach is that our topological trivialisations are global in the base.