Effective computation of the general component of the jet scheme

• Mario Morán Cañó ^[1] ; Julien Sebag ^[2]
  1. [1] University of Oklahoma

     University of Oklahoma

     Estados Unidos

     
  2. [2] Université de Rennes 1
• Localización: EACA 2022: XVII Encuentro de Álgebra Computacional y Aplicaciones / coord. por Carlos Galindo Pastor, Philippe Giménez, Fernando Javier Hernando Carrillo, F. Monserrat Delpalillo, Julio José Moyano Fernández, 2023, ISBN 978-84-19647-46-7, págs. 127-130
• Idioma: inglés
• Enlaces
  • Texto Completo Libro
• Resumen

  • Let k be a perfect field. Let X be an integral k-variety. Let m ∈ N. Westudy, from the theoretical and computational points of view, the component Gm(X) of the jet scheme Lm(X) defined to be the Zariski closure of the set of truncated arcs with a regular base-point. When char(k) = 0 and X is a weighted homogeneous plane curve singularity, we provide a Gröbner basis of the ideal N1 (X) defining G1 (X) as a reduced closed subscheme of L1 (X). More generally, we prove that Gm(X) can be described fromany smooth birational model of X. When X is supposed to be affine embedded in ANk, this description provides an algorithm, valid for fields of arbitrary characteristic, which computes a Gröbner basis of a presentation of Gm(X) in A(m+1)N k from the datum of a given explicit smooth affine birational model of X. We finally present some applications.