The Denef-Loeser series for toric surface singularities
Monique Lejeune-Jalabert
Université de Versailles Saint-Quentin, Versailles, FranceAna J. Reguera
Universidad de Valladolid, Spain
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Abstract
Let denote the set of formal arcs going through a singular point of an algebraic variety defined over an algebraically closed field of characteristic zero. In the late sixties, J. Nash has observed that for any nonnegative integer , the set of -jets of arcs in 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 in some suitable localization of the Grothendieck ring of algebraic varieties over is a rational function. We compute this function for normal toric surface singularities.
Cite this article
Monique Lejeune-Jalabert, Ana J. Reguera, The Denef-Loeser series for toric surface singularities. Rev. Mat. Iberoam. 19 (2003), no. 2, pp. 581–612
DOI 10.4171/RMI/361