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Some Numerical Criteria for the Nash Problem on Arcs for Surfaces

2008
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Nagoya mathematical journal
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Let (X, O) be a germ of a normal surface singularity, π: → X be the minimal resolution of singularities and let A = (ai,j ) be the n × n symmetrical intersection matrix of the exceptional set of In an old preprint Nash proves that the set of arcs on a surface singularity is a scheme , and defines a map from the set of irreducible components of to the set of exceptional components of the minimal resolution of singularities of (X,O). He proved that this map is injective and ask if it is

doi:10.1017/s0027763000025897
fatcat:ulanl7uvezhbzhksng27bfk7g4