Arcs on rational double points in arbitrary characteristic

TL;DR

This paper proves the Nash problem for two-dimensional rational double points across all characteristics by explicitly computing arc families through these singularities.

Contribution

It provides a complete proof of the Nash problem for rational double points in arbitrary characteristic using direct arc family computations.

Findings

Nash problem holds for rational double points in all characteristics

Explicit arc family computations are used in the proof

The result extends known cases to arbitrary characteristic

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.