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Journal of Topology Advance Access originally published online on November 26, 2008
Journal of Topology 2008 1(4):879-909; doi:10.1112/jtopol/jtn024
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© 2008 London Mathematical Society

Equisingularity at the normalisation

Javier Fernández de Bobadilla

ICMAT (CSIC-Complutense-Autónoma- Carlos III), Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense, Plaza de Ciencias 3, 28040 Madrid, Spain javier@mat.csic.es

María Pe Pereira

Departamento de Álgebra, Facultad de Ciencias Matemáicas, Universidad Complutense, Plaza de Ciencias 3, 28040 Madrid, Spain maria.pe@mat.ucm.es


  Abstract

We look at topological equisingularity of a holomorphic family of reduced mapping germs Formula 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.

Received March 26, 2007.

2000 Mathematics Subject Classification 32S25, 32S50 (primary)

Dedicated to José María Montesions, on the occasion of his 60th birthday.

The first author was supported by Ramon y Cajal contract. The second author was supported by FPI contract of Ministerio de Educación y Ciencia of Spain and cofinanced by the ESF. Both authors were also supported by the Spanish project MTM2004-08080-C02-01.


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