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arXiv · 1011.2950

Geometric motivic Poincaré series of quasi-ordinary singularities

Helena Cobo Pablos·Pedro Daniel Gonzalez Perez
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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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Helena Cobo Pablos, Pedro Daniel Gonzalez Perez. 2010-11-12. Geometric motivic Poincaré series of quasi-ordinary singularities. https://doi.org/10.1017/s0305004110000101

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