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

Abstract

top
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.

How to cite

top

Lejeune-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 ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.