The Denef-Loeser series for toric surface singularities

  • Monique Lejeune-Jalabert

    Université de Versailles Saint-Quentin, Versailles, France
  • Ana J. Reguera

    Universidad de Valladolid, Spain


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