On the Nash Problem over 3-Fold Terminal Singularities of Type cAx/2

2025/12/20 by Keng-Hung Steven Lin, Lin, Keng-Hung Steven
Mathematics · #14E18 (Primary) 14E15 #14E30 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.18243

openalex publication_date 2025/12/20 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

Abstract

We study Nash valuations on 3-fold terminal singularities, especially in type cAx/2. We find that, in type cAx/2, exceptional prime divisors computing the minimal discrepancy (which is 1/2 in this case) induce Nash valuations. We conjecture this in general for all 3-fold terminal singularities, and provide some evidence in the Gorenstein case.

Citations

• Minimal resolutions of threefolds
• The Nash problem for torus actions of complexity one
• On the Nash problem for terminal threefolds of type cA/r
• The space of arcs of an algebraic variety
• Explicit resolution of three dimensional terminal singularities
• Arc spaces of cA-type singularities
• Three-dimensional counter-examples to the Nash problem
• Nash problem for surfaces
• Exceptional divisors which are not uniruled belong to the image of the Nash map
• Jet schemes and singularities
• The Nash problem on arc families of singularities

Related

• On the Nash problem for terminal threefolds of type cA/r
• Three-dimensional counter-examples to the Nash problem
• The Nash problem for torus actions of complexity one
• Résolution du problème des arcs de Nash pour une famille d'hypersurfaces quasi-rationnelles
• On a Computational Approach to the Nash Blowup Problem