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The zeta function of a quasi-ordinary singularity

Published online by Cambridge University Press:  04 December 2007

Lee J. McEwan  and
András Némethi
Lee J. McEwan
Affiliation:
Department of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, USAmcewan@math.ohio-state.edu, nemethi@math.ohio-state.edu
András Némethi
Affiliation:
Department of Mathematics, Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, USAmcewan@math.ohio-state.edu, nemethi@math.ohio-state.edu
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Abstract

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We prove that the zeta function of an irreducible hypersurface quasi-ordinary singularity f equals the zeta function of a plane curve singularity g. If the local coordinates $(x_1,\dots,x_{d+1})$ of f are ‘nice’, then $g=f(x_1,0,\dots,0,x_{d+1})$. Moreover, the Puiseux pairs of g can also be recovered from (any set of) distinguished tuples of f.

Keywords

quasi-ordinary singularitiesMilnor fibermonodromyzeta functionNewton polyhedrontoric resolution14B0532Sxx
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 3 , May 2004 , pp. 667 - 682
Copyright
Foundation Compositio Mathematica 2004