Mathematics – Algebraic Geometry
Scientific paper
2006-12-07
Mathematics
Algebraic Geometry
26 pages, 2 figures
Scientific paper
We look at topological equisingularity of a holomorphic family of reduced mapping germs f_t:(C^3,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 f_t 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.
de Bobadilla Javier Fernandez
Pereira Maria Pe
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