Geometriae Dedicata

, Volume 173, Issue 1, pp 143–162 | Cite as

The boundary of the Milnor fibre of complex and real analytic non-isolated singularities

  • Javier Fernández de Bobadilla
  • Aurélio Menegon Neto
Original Paper

Abstract

Let \(f\) and \(g\) be holomorphic function-germs vanishing at the origin of complex analytic germs of dimension three. Suppose that they have no common irreducible component and that the real analytic map-germ \(f\bar{g}\) has an isolated critical value at 0. We give necessary and sufficient conditions for the real analytic map-germ \(f\bar{g}\) to have a Milnor fibration and we prove that in this case the boundary of its Milnor fibre is a Waldhausen manifold. As an intermediate milestone we describe geometrically the Milnor fibre of map-germs of the form \(f\bar{g}\) defined in a complex surface germ, and we prove an A’Campo-type formula for the zeta function of its monodromy.

Keywords

Milnor fibration Non-isolated singularity Real singularity  Waldhausen manifold A’Campo formula Monodromy  Zeta function Vanishing zone 

Mathematics Subject Classification (2000)

Primary: 14B05 14J17 14E15 32S05 32S25 32S45 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Javier Fernández de Bobadilla
    • 1
  • Aurélio Menegon Neto
    • 2
  1. 1.ICMAT, CSIC-Complutense-Autónoma-Carlos IIIMadridSpain
  2. 2.Departamento de MatemáticaUniversidade Federal da ParaíbaJoão PessoaBrazil

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