Equisingularity at the Normalisation
نویسندگان
چکیده
We look at topological equisingularity of a holomorphic family of reduced mapping germs ft : (C , O) → C over a contractible base T having non-isolated singularities, by means of their normalisations. The relation between surfaces in C with non-isolated singularities and normal surface singularities via the normalisation is a very convenient way of exchanging information between both categories. This has been already exploited fruitfully by T. de Jong and D. van Straten in order to study deformations of singularities [6], [7], [8]. Moreover we apply our results to the study of topological A-equisingularity of parametrised surfaces. The main observation is that the normalisation of a parametrised surface coincides with the parametrisation itself. We introduce the notion of Equisingularity at the normalisation for a family ft (see Definition 2). It turns out that in many cases, equisingularity at the normalisation characterises topological embedded equisingularity and R-equisingularity. More precisely we prove the following theorem:
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