A solution to the Nash problem of arcs for rational double points \(D_n\). (Résolution du probléme des arcs de Nash pour les points doubles rationnels \(D_{n}\).) (French) Zbl 1072.14004

Summary: This note deals with the Nash problem, which claims that there are as many families of arcs on a singular germ of surface \(U\) as there are essential components of the exceptional divisor in the desingularisation of this singularity. We prove that this claim holds for the rational double points \(D_n (n \geqslant 4)\).


14B05 Singularities in algebraic geometry
14J17 Singularities of surfaces or higher-dimensional varieties
32S25 Complex surface and hypersurface singularities
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