COORDINATES AT STABLE POINTS OF THE SPACE OF ARCS
Résumé
Let X be a variety over a field k and let X∞ be its space of arcs. Let P be the stable point of X∞ defined by a divisorial valuation ν on X. Assuming char k = 0, if X is smooth at the center of P, we make a study of the graded algebra associated to ν and define a finite set whose elements generate a localization of the graded algebra modulo étale covering. This provides an explicit description of a minimal system of generators of the local ring O of X∞ at P. If X is singular, we obtain generators of P / P^2 and conclude that the embedding dimension of the completion of O is less or equal to k^+ 1 where k^ is the Mather discrepancy of X with respect to ν .
Domaines
Géométrie algébrique [math.AG]
Fichier principal
Coordinates at stable points of the space of arcs.pdf (223.69 Ko)
Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...