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Geometric motivic Poincaré series of quasi-ordinary singularities

Published online by Cambridge University Press:  24 March 2010

HELENA COBO PABLOS  and
PEDRO D. GONZÁLEZ PÉREZ
HELENA COBO PABLOS
Affiliation:
Department of Mathematics, University of Leuven, Celestijnenlaan 200B, B-3001 Leuven-Heverlee, Belgium. e-mail: Helena.Cobo@wis.kuleuven.be
PEDRO D. GONZÁLEZ PÉREZ
Affiliation:
ICMAT. Depto. Álgebra. Universidad Complutense de Madrid, Plaza de las Ciencias 3, 28040, Madrid, Spain. e-mail: pgonzalez@mat.ucm.es
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Abstract

The geometric motivic Poincaré series of a germ (S, 0) of complex algebraic variety takes into account the classes in the Grothendieck ring of the jets of arcs through (S, 0). Denef and Loeser proved that this series has a rational form. We give an explicit description of this invariant when (S, 0) is an irreducible germ of quasi-ordinary hypersurface singularity in terms of the Newton polyhedra of the logarithmic jacobian ideals. These ideals are determined by the characteristic monomials of a quasi-ordinary branch parametrizing (S, 0).

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 1 , July 2010 , pp. 49 - 74
Copyright
Copyright © Cambridge Philosophical Society 2010

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