The nash problem on arc families of singularities

Shihoko Ishii; János Kollár

doi:10.1215/S0012-7094-03-12034-7

The nash problem on arc families of singularities

Shihoko Ishii
, János Kollár

Mathematics

Research output: Contribution to journal › Article › peer-review

76 Scopus citations

Abstract

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)
Pages (from-to)	601-620
Number of pages	20
Journal	Duke Mathematical Journal
Volume	120
Issue number	3
DOIs	https://doi.org/10.1215/S0012-7094-03-12034-7
State	Published - Dec 1 2003

All Science Journal Classification (ASJC) codes

General Mathematics

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AB - 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.

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JO - Duke Mathematical Journal

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The nash problem on arc families of singularities

Abstract

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