Duke Mathematical Journal

The Nash problem on arc families of singularities

János Kollár and Shihoko Shihoko Ishii

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Nash [21] 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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Duke Math. J. Volume 120, Number 3 (2003), 601-620.

First available in Project Euclid: 16 April 2004

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Zentralblatt MATH identifier

Primary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] 14M25: Toric varieties, Newton polyhedra [See also 52B20] 14J10: Families, moduli, classification: algebraic theory
Secondary: 14J17: Singularities [See also 14B05, 14E15] 14B20: Formal neighborhoods


Shihoko Ishii, Shihoko; Kollár, János. The Nash problem on arc families of singularities. Duke Math. J. 120 (2003), no. 3, 601--620. doi:10.1215/S0012-7094-03-12034-7. http://projecteuclid.org/euclid.dmj/1082137355.

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