Coordinates at stable points of the space of arcs
type: Item
instance of: scholarly article
title: Coordinates at stable points of the space of arcs
zbMATH Open document ID: 1388.13001
published in: Journal of Algebra
publication date: 2017-11-15T00:00:00Z
review text: Let \(X\) be a variety over a field \(k\) of characteristic 0 and let \(X_\infty\) be its space of arcs (see [\textit{J. F. Nash jun.}, Duke Math. J. 81, No. 1, 31--38 (1995; Zbl 0880.14010)]). Let \(P_E\) be the stable point of \(X_\infty\) defined by a divisorial valuation \(\nu_E\) on \(X\). The author investigates the analytic structure of the local ring \(\mathcal O_{X_\infty, P_E}\). In particular, she finds a suitable coordinate representation for the completion of this ring with respect to its maximal ideal, computes generators (a regular system of parameters) of the ring, its embedding dimension, and so on.
reviewed by: Aleksandr G. Aleksandrov
Mathematics Subject Classification ID: 13A02
Mathematics Subject Classification ID: 13A18
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14B25
Mathematics Subject Classification ID: 14E15
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 32S05
zbMATH DE Number: 6807250
zbMATH Keywords: space of arcs
zbMATH Keywords: divisorial valuation
zbMATH Keywords: graded algebra
zbMATH Keywords: henselization
zbMATH Keywords: étale coverings
author: Ana J. Reguera-López
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2017.09.031
OpenAlex ID: W2761006692
cites work: On the Valuations Centered in a Local Domain
cites work: Q3994901
cites work: Minimal generating system, essential divisors and \(G\)-desingularisation of toric varieties
cites work: Germs of arcs on singular algebraic varieties and motivic integration
cites work: Singularities with respect to Mather-Jacobian discrepancies
cites work: Q3622200
cites work: Three-dimensional counter-examples to the Nash problem
cites work: Jacobian discrepancies and rational singularities
cites work: Divisorial valuations via arcs
cites work: Q4945008
cites work: Q4143433
cites work: Mather discrepancy and the arc spaces
cites work: The Nash problem on arc families of singularities
cites work: Arc spaces of cA-type singularities
cites work: Exceptional divisors that are not uniruled belong to the image of the Nash map
cites work: Approximate roots of a valuation and the Pierce-Birkhoff conjecture
cites work: Q4895029
cites work: Anneaux locaux henséliens
cites work: Image of the Nash map in terms of wedges.
cites work: A curve selection lemma in spaces of arcs and the image of the Nash map
cites work: Towards the singular locus of the space of arcs
cites work: Valuations in Function Fields of Surfaces
cites work: Overweight deformations of affine toric varieties and local uniformization
cites work: Q3413424
DOI: 10.1016/J.JALGEBRA.2017.09.031
description: scientific article; zbMATH DE number 6807250