Arcs on rational double points in arbitrary characteristic

2025/08/17 by de Fernex, Tommaso, Wang, Shih-Hsin · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14E18 #Secondary 14J17

paper · doi:10.48550/arxiv.2508.12423

Abstract

We prove that the Nash problem holds for two-dimensional rational double points in all characteristics. The proof is based on a direct computation of the families of arcs through these singularities.

Citations

• Families of jets of arc type and higher (co)dimensional Du Val singularities
• On the Nash problem for surfaces in positive characteristic
• The space of arcs of an algebraic variety
• Three-dimensional counter-examples to the Nash problem
• Nash problem for surfaces
• Résolution du problème des arcs de Nash pour une famille d'hypersurfaces quasi-rationnelles
• Nash problem for surface singularities is a topological problem
• Jet schemes and singularities
• The Nash problem on arc families of singularities

Cited by

• Jet Schemes, Newton Polygons and Continued Fractions

Related

• The Nash problem of arcs and the rational double point E₆
• Résolution du problème des arcs de Nash pour une famille d'hypersurfaces quasi-rationnelles
• The Nash problem on arc families of singularities
• The Nash problem from a geometric and topological perspective
• Resolution du probleme des arcs de Nash pour les points doubles rationnels