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On the Milnor Fiber of a Quasi-ordinary Surface Singularity

Published online by Cambridge University Press:  20 November 2018

Chunsheng Ban ,
Lee J. McEwan  and
András Némethi
Chunsheng Ban
Affiliation:
Department of Mathematics Ohio State University 231 West 18th Avenue Columbus, Ohio U.S.A., email: cban@math.ohio-state.edu
Lee J. McEwan
Affiliation:
Department of Mathematics Ohio State University 231 West 18th Avenue Columbus, Ohio U.S.A., email: mcewan@math.ohio-state.edu
András Némethi
Affiliation:
Department of Mathematics Ohio State University 231 West 18th Avenue Columbus, Ohio U.S.A., email: nemethi@math.ohio-state.edu
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Abstract

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We verify a generalization of (3.3) from [Lê73] proving that the homotopy type of the Milnor fiber of a reduced hypersurface singularity depends only on the embedded topological type of the singularity. In particular, using [Zariski68, Lipman83, Oh93, Gau88] for irreducible quasi-ordinary germs, it depends only on the normalized distinguished pairs of the singularity. The main result of the paper provides an explicit formula for the Euler-characteristic of the Milnor fiber in the surface case.

Keywords

14B0514E1532S55
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 54 , Issue 1 , 01 February 2002 , pp. 55 - 70
Copyright
Copyright © Canadian Mathematical Society 2002

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