Arcs on rational double points in arbitrary characteristic

Tommaso de Fernex; Shih-Hsin Wang

doi:10.48550/arxiv.2508.12423

August 17, 2025Open Access

Arcs on rational double points in arbitrary characteristic

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Key Points

The Nash problem is confirmed for rational double points, highlighting new insights into singularities.
Key evidence shows that the proof is based on direct computations of arc families, revealing important details.
The method involves calculations through two-dimensional rational double points, establishing a robust foundation.
This finding suggests broader implications for the study of curves at singularities in various mathematical contexts.

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Implication

We prove the Nash problem holds for rational double points in all characteristics, indicating a breakthrough in understanding singularities.

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.

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Fernex et al. (2025) studied this question.

synapsesocial.com/papers/68d913a34ddcf71ba560b7fc https://doi.org/10.48550/arxiv.2508.12423

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Arcs on rational double points in arbitrary characteristic

Key Points

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Implication

Abstract

Discussion

Cite This Study

Arcs on rational double points in arbitrary characteristic

Key Points

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Implication

Abstract

Discussion

Cite This Study

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