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Motivic Poincaré series, toric singularities and logarithmic Jacobian ideals

 

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Opened Access Motivic Poincaré series, toric singularities and logarithmic Jacobian ideals
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Author: Cobo Pablos, Helena
González Pérez, Pedro Daniel
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2012
Published in: Journal of Algebraic Geometry, 21 (3), 495-529.
Document type: Article
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.
Cite: Cobo Pablos, H. y González Pérez, P.D. (2012). Motivic Poincaré series, toric singularities and logarithmic Jacobian ideals. Journal of Algebraic Geometry, 21 (3), 495-529.
Size: 416.7Kb
Format: PDF

URI: http://hdl.handle.net/11441/47596

DOI: 10.1090/S1056-3911-2011-00567-5

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