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oai:docta.ucm.es:20.500.14352/419302023-08-28T06:07:08Zcom_20.500.14352_14col_20.500.14352_15

Geometric motivic Poincaré series of quasi-ordinary singularities González Pérez, Pedro Daniel Cobo Pablos, Maria Helena 512.7 Arc space Quasi-ordinary singularities Geometria algebraica 1201.01 Geometría Algebraica Geometric motivic Poincaré series of a germ at a singular point of complex algebraic variety describes the truncated images of the space of arcs through the singular point. Denef and Loeser proved that it has a rational form. In this paper, the authors study an irreducible germ of quasi-ordinary hypersurface singularities and introduce the notion of logarithmic Jacobian ideals. The main result of this paper is to give the explicit rational form of geometric motivic Poincaré series of such a singularity in terms of the lattice and the Newton polyhedra of the logarithmic Jacobian ideals. Ministerio de Educación y Ciencia (MEC) Fundación Caja Madrid Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T00:05:22Z 2023-06-20T00:05:22Z 2010 journal article https://hdl.handle.net/20.500.14352/41930 1469-8064 10.1017/S0305004110000101 eng MTM2004-08080-C02-01 restricted access application/pdf application/pdf Cambridge University Press