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September, 2003 The Denef-Loeser series for toric surface singularities
Monique Lejeune-Jalabert, Ana J. Reguera
Rev. Mat. Iberoamericana 19(2): 581-612 (September, 2003).


Let $H$ denote the set of formal arcs going through a singular point of an algebraic variety $V$ defined over an algebraically closed field $k$ of characteristic zero. In the late sixties, J. Nash has observed that for any nonnegative integer $s$, the set $j^s(H)$ of $s$-jets of arcs in $H$ is a constructible subset of some affine space. Recently (1999), J. Denef and F. Loeser have proved that the Poincar\'{e} series associated with the image of $j^s(H)$ in some suitable localization of the Grothendieck ring of algebraic varieties over $k$ is a rational function. We compute this function for normal toric surface singularities.


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Monique Lejeune-Jalabert. Ana J. Reguera. "The Denef-Loeser series for toric surface singularities." Rev. Mat. Iberoamericana 19 (2) 581 - 612, September, 2003.


Published: September, 2003
First available in Project Euclid: 8 September 2003

zbMATH: 1058.14006
MathSciNet: MR2023199

Primary: 14B05 , 14J17 , 14M25

Keywords: arc spaces , Denef-Loeser series , toric surfaces

Rights: Copyright © 2003 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.19 • No. 2 • September, 2003
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