The Nash problem on arc families of singularities

Details The Nash problem on arc families of singularities The Nash problem on arc families of singularities

2002-07-19

arxiv.org/abs/math/0207171v2

Mathematics

Algebraic Geometry

17 pages

Scientific paper

Nash proved that every irreducible component of the space of arcs through a
singularity corresponds to an exceptional divisor that occurs on every
resolution. He asked if the converse also holds: does every such exceptional
divisor correspond to an arc family? We prove that the converse holds for toric
singularities but fails in general.

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