# The Denef-Loeser series for toric surface singularities.

Monique Lejeune-Jalabert; Ana J. Reguera

Revista Matemática Iberoamericana (2003)

- Volume: 19, Issue: 2, page 581-612
- ISSN: 0213-2230

## Access Full Article

top## Abstract

top## How to cite

topLejeune-Jalabert, Monique, and Reguera, Ana J.. "The Denef-Loeser series for toric surface singularities.." Revista Matemática Iberoamericana 19.2 (2003): 581-612. <http://eudml.org/doc/39676>.

@article{Lejeune2003,

abstract = {Let H denote the set of formal ares going through a singular point of an algebraic variety V defined over an algebraically closed field k of charactcristic zcro. In the late sixties, J, Nash has observed that for any nonnegative integer s, the set js(H) of s-jets of ares in H is a constructible subset of some affine space. Recently (1999), J. Denef and F. Loeser have proved that the Poincaré series associated with the image of js(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.},

author = {Lejeune-Jalabert, Monique, Reguera, Ana J.},

journal = {Revista Matemática Iberoamericana},

keywords = {Geometría algebraica; Singularidades; Toros geométricos; Series de potencias; arc spaces; continued fraction; Nash blowing-up},

language = {eng},

number = {2},

pages = {581-612},

title = {The Denef-Loeser series for toric surface singularities.},

url = {http://eudml.org/doc/39676},

volume = {19},

year = {2003},

}

TY - JOUR

AU - Lejeune-Jalabert, Monique

AU - Reguera, Ana J.

TI - The Denef-Loeser series for toric surface singularities.

JO - Revista Matemática Iberoamericana

PY - 2003

VL - 19

IS - 2

SP - 581

EP - 612

AB - Let H denote the set of formal ares going through a singular point of an algebraic variety V defined over an algebraically closed field k of charactcristic zcro. In the late sixties, J, Nash has observed that for any nonnegative integer s, the set js(H) of s-jets of ares in H is a constructible subset of some affine space. Recently (1999), J. Denef and F. Loeser have proved that the Poincaré series associated with the image of js(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.

LA - eng

KW - Geometría algebraica; Singularidades; Toros geométricos; Series de potencias; arc spaces; continued fraction; Nash blowing-up

UR - http://eudml.org/doc/39676

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.