On the Milnor Fiber Boundary of a Quasi-Ordinary Surface

Gary Kennedy and Lee J. McEwan

Journal of Singularities
volume 19 (2019), 34-52

Received: 6 January 2019. Received in revised form: 5 June 2019

DOI: 10.5427/jsing.2019.19c

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Abstract:

We give a recursive formula, expressed in terms of the characteristic tuples, for the Betti numbers of the boundary of the Milnor fiber of an irreducible quasi-ordinary surface S which is reduced in the sense of Lipman. The singular locus of S consists of two components, and for each component we introduce a sequence of increasingly simpler surfaces. Our recursion depends on a detailed comparison of these two sequences. In the penultimate section, we indicate how we expect pieces of these associated surfaces to glue together to reconstruct the Milnor fiber of S and its boundary.


Author(s) information:

Gary Kennedy Lee J. McEwan
Department of Mathematics Department of Mathematics
The Ohio State University The Ohio State University
1760 University Drive 1760 University Drive
Mansfield, Ohio 44906 USA Mansfield, Ohio 44906 USA
email: kennedy.28@osu.edu email: mcewan.1@osu.edu