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Families of arcs on rational surface singularities

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Abstract

We consider the spaceH of arcs on a rational surface singularity (S, P), with the proalgebraic structure induced by the truncation maps. We introduce some sets of arcs by imposing valuative conditions and we prove that they are closed subsets ofH. This leads to give a sufficient condition in order to have an affirmative answer for the problem of Nash. We conclude the solution of the problem for the minimal surface singularities.

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Authors and Affiliations

  1. Departmento de Álgebra y Geometría Facultad de Ciencias, Universidad de Valladolid, 47005, Valladolid, Spain

    A. J. Reguera

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  1. A. J. Reguera
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Supported by D.G.I.C.Y.T. PB91-0210-C02-01

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Reguera, A.J. Families of arcs on rational surface singularities. Manuscripta Math 88, 321–333 (1995). https://doi.org/10.1007/BF02567826

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  • DOI: https://doi.org/10.1007/BF02567826

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