Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Motivic Poincaré series, toric singularities and logarithmic Jacobian ideals


Authors: H. Cobo Pablos and P. D. González Pérez
Journal: J. Algebraic Geom. 21 (2012), 495-529
DOI: https://doi.org/10.1090/S1056-3911-2011-00567-5
Published electronically: August 22, 2011
MathSciNet review: 2914802
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Abstract | References | Additional Information

Abstract: The geometric motivic Poincaré series of a variety, which was introduced by Denef and Loeser, takes into account the classes in the Grothendieck ring of the sequence of jets of arcs in the variety. Denef and Loeser proved that this series has a rational form. We describe it in the case of an affine toric variety of arbitrary dimension. The result, which provides an explicit set of candidate poles, is expressed in terms of the sequence of Newton polyhedra of certain monomial ideals, which we call logarithmic Jacobian ideals, associated to the modules of differential forms with logarithmic poles outside the torus of the toric variety.


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Additional Information

H. Cobo Pablos
Affiliation: Depto. Algebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de las Ciencias 3. 28040, Madrid, Spain
Email: hcobopab@mat.ucm.es

P. D. González Pérez
Affiliation: Instituto de Ciencias Matemáticas-CSIC-UAM-UC3M-UCM, Depto. Algebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de las Ciencias 3. 28040, Madrid, Spain
Email: pgonzalez@mat.ucm.es

DOI: https://doi.org/10.1090/S1056-3911-2011-00567-5
Received by editor(s): September 17, 2009
Received by editor(s) in revised form: March 18, 2010
Published electronically: August 22, 2011
Additional Notes: The first author is supported by a grant of Fundación Caja Madrid. The second author is supported by Programa Ramón y Cajal of Ministerio de Educación y Ciencia (MEC), Spain. Both authors are supported by MTM2007-6798-C02-02 grant of MEC

American Mathematical Society