Nash proved that every irreducible component of the space of arcs through a singularity corresponds to an exceptional divisor that appears 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.
|Original language||English (US)|
|Number of pages||20|
|Journal||Duke Mathematical Journal|
|State||Published - Dec 1 2003|
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