Kodai Mathematical Journal

The Nash problem of arcs and the rational double point E6

Camille Plénat and Mark Spivakovsky

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Abstract

This paper deals with the Nash problem, which consists in proving that the number of families of arcs on a germ of a normal isolated singularity coincides with the number of essential components of the exceptional set in any resolution of this singularity. We propose a program for an affirmative solution of the Nash problem for special types of normal isolated hypersurface singularities. We illustrate this program by giving an affirmative solution of the Nash problem for the rational double point E6. We also prove some results on the algebraic structure of the space of k-jets of an arbitrary hypersurface singularity and apply them to the specific case of E6.

Article information

Source
Kodai Math. J., Volume 35, Number 1 (2012), 173-213.

Dates
First available in Project Euclid: 29 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1333027261

Digital Object Identifier
doi:10.2996/kmj/1333027261

Mathematical Reviews number (MathSciNet)
MR2911273

Zentralblatt MATH identifier
1271.14006

Citation

Plénat, Camille; Spivakovsky, Mark. The Nash problem of arcs and the rational double point E 6. Kodai Math. J. 35 (2012), no. 1, 173--213. doi:10.2996/kmj/1333027261. https://projecteuclid.org/euclid.kmj/1333027261


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