Disentanglements and Whitney equisingularity

• Autores: Kevin Houston
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 3, 2007, págs. 663-681
• Idioma: inglés
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• Resumen

  • A classical theorem of Briançon, Speder and Teissier states that a family of isolated hypersurface singularities is Whitney equisingular if, and only if, the mu*-sequence for a hypersurface is constant in the family. This paper shows that similar results are true for families of finitely A-determined map-germs from Cn to C3, where n=2 or 3. Rather than the Milnor fibre we use the disentanglement of a map, and since a disentanglement can be viewed as a section of a stable discriminant we can apply Damon's theory which defines an analogue of the mu*-sequence. The constancy of this sequence is equivalent to Whitney equisingularity of the family in the n=2 case. For the other case it is shown, using extra information, that the image of the family is Whitney equisingular.