The nash problem on arc families of singularities

Shihoko Ishii, János Kollár

Research output: Contribution to journalArticlepeer-review

65 Scopus citations


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 languageEnglish (US)
Pages (from-to)601-620
Number of pages20
JournalDuke Mathematical Journal
Issue number3
StatePublished - Dec 1 2003

All Science Journal Classification (ASJC) codes

  • General Mathematics


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