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Revista Matemática Complutense

, Volume 29, Issue 1, pp 225–239 | Cite as

The Milnor fiber of the singularity \(f(x,y) + zg(x,y) = 0\)

  • Baldur SigurðssonEmail author
Article
  • 109 Downloads

Abstract

We give a description of the Milnor fiber and the monodromy of a singularity of the form \(f+zg = 0\), where f and g define germs of plane curve singularities and have no common components. In particular, this gives a description of the boundary of the Milnor fiber. The description depends only on the topological type of the two plane curve germs defined by f and g. As a corollary, we give a simple formula for the monodromy zeta function and the Euler characteristic of the fiber in terms of an embedded resolution of f and g.

Keywords

Nonisolated hypersurface singularities Milnor fiber  Monodromy zeta function 

Mathematics Subject Classification

Primary 32S05 32S25 32S55 58K10 Secondary 14Bxx  32Sxx 

Notes

Acknowledgments

The author is supported by the Ph.D. program of the CEU, Budapest and by the ‘Lendület’ and ERC program ‘LTDBud’ at Rényi Institute.

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Copyright information

© Universidad Complutense de Madrid 2015

Authors and Affiliations

  1. 1.Alfréd Rényi Institute of MathematicsBudapestHungary
  2. 2.Department of MathematicsCentral European UniversityBudapestHungary

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