Duke Mathematical Journal

The Nash problem on arc families of singularities

János Kollár and Shihoko Shihoko Ishii

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Abstract

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.

Article information

Source
Duke Math. J. Volume 120, Number 3 (2003), 601-620.

Dates
First available: 16 April 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1082137355

Digital Object Identifier
doi:10.1215/S0012-7094-03-12034-7

Mathematical Reviews number (MathSciNet)
MR2030097

Subjects
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

Citation

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


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