{"paper":{"title":"The Nash problem on arcs for surface singularities","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Marcel Morales","submitted_at":"2006-09-22T07:31:39Z","abstract_excerpt":"Let $(X,O)$ be a germ of a normal surface singularity, $\\pi : \\tilde X\\longrightarrow X$ be the minimal resolution of singularities and let $A=(a_{i,j})$ be the $n\\times n$ symmetrical intersection matrix of the exceptional set of $\\tilde X$. In an old preprint Nash proves that the set of arcs on a surface singularity is a scheme ${\\cal H}$, and defines a map ${\\cal N}$ from the set of irreducible components of ${\\cal H}$ to the set of exceptional components of the minimal resolution of singularities of $(X,O)$. He proved that this map is injective and ask if it is surjective. In this paper we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609629","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}