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

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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.

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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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Correspondence to Baldur Sigurðsson.

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Sigurðsson, B. The Milnor fiber of the singularity \(f(x,y) + zg(x,y) = 0\) . Rev Mat Complut 29, 225–239 (2016). https://doi.org/10.1007/s13163-015-0179-5

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  • DOI: https://doi.org/10.1007/s13163-015-0179-5

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