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Exceptional divisors that are not uniruled belong to the image of the Nash map

Part of: Local theory

Published online by Cambridge University Press:  13 December 2011

Monique Lejeune-Jalabert  and
Ana J. Reguera
Monique Lejeune-Jalabert
Affiliation:
Centre National de la Recherche Scientifique, Laboratoire de Mathématiques de Versailles, UMR8100, CNRS-UVSQ, Université de Versailles, Saint-Quentin, Bâtiment Fermat, 45 Avenue des Etats-Unis, F-78035 Versailles Cedex, France (lejeune@math.uvsq.fr)
Ana J. Reguera
Affiliation:
Departamento de Álgebra, Geometría y Topología, Universidad de Valladolid, Prado de la Magdalena s/n, 47005 Valladolid, Spain (areguera@agt.uva.es)
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Abstract

We prove that, if X is a variety over an uncountable algebraically closed field k of characteristic zero, then any irreducible exceptional divisor E on a resolution of singularities of X which is not uniruled, belongs to the image of the Nash map, i.e. corresponds to an irreducible component of the space of arcs on X centred in Sing X. This reduces the Nash problem of arcs to understanding which uniruled essential divisors are in the image of the Nash map, more generally, how to determine the uniruled essential divisors from the space of arcs.

Keywords

arcswedgesresolution of singularitiesNash mapessential divisorsuniruled variety

MSC classification

Secondary: 14B05: Singularities
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 11 , Issue 2 , April 2012 , pp. 273 - 287
Copyright
Copyright © Cambridge University Press 2012

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