The Local Nash problem on arc families of singularities

2005/07/26 by Shihoko Ishii, Ishii, Shihoko
Mathematics · #14J17 #14M25 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG #msc:14J17 #msc:14M25

paper · pdf · doi:10.48550/arxiv.math/0507530

to appear in Annales de l'Institute Fourier

arxiv created 2005/07/26 · openalex publication_date 2005/07/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper shows the affirmative answer to the local Nash problem for a toric singularity and analytically pretoric singularity. As a corollary we obtain the affirmative answer to the local Nash problem for a quasi-ordinary singularity.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

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• The Nash problem on arc families of singularities
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• The embedded Nash problem in singular spaces: the case of surfaces