{"paper":{"title":"Resolutions and deformations of cyclic quotient surface singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Various independently developed results on minimal resolutions of cyclic quotient singularities unify into one coherent exposition.","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kohei Sato, Meral Tosun, Yukari Ito","submitted_at":"2026-04-06T06:47:02Z","abstract_excerpt":"In this paper, we investigate the relations among various results concerning the minimal resolution of cyclic quotient singularities of the form $\\mathbb{C}^2/G$. We refer to these as \"bamboo-type\" singularities, since the dual graphs of the exceptional curves in their resolutions resemble the shape of bamboo. We present classical results on the minimal resolution of singularities, the $G$-Hilbert scheme, the generalized McKay correspondence, deformations of singularities, and quiver varieties. These results have been obtained independently in different contexts, and here we provide a unified "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We investigate the relations among various results concerning the minimal resolution of cyclic quotient singularities of the form C^2/G ... present classical results on the minimal resolution of singularities, the G-Hilbert scheme, the generalized McKay correspondence, deformations of singularities, and quiver varieties ... provide a unified exposition enriched with numerous examples.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That independently developed results from different contexts can be unified into a single coherent exposition without introducing inconsistencies, oversimplifications, or loss of technical detail.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Unified survey linking resolutions, Hilbert schemes, McKay correspondence, and deformations for bamboo-type cyclic quotient singularities.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Various independently developed results on minimal resolutions of cyclic quotient singularities unify into one coherent exposition.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"38e4ba5583b9aace1688ce0ea057d3ab1fe4f82e05f16ac8fd64e68f58e69471"},"source":{"id":"2604.04472","kind":"arxiv","version":2},"verdict":{"id":"624da94a-8541-4106-964f-c3bdd14db1e2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T19:50:44.558661Z","strongest_claim":"We investigate the relations among various results concerning the minimal resolution of cyclic quotient singularities of the form C^2/G ... present classical results on the minimal resolution of singularities, the G-Hilbert scheme, the generalized McKay correspondence, deformations of singularities, and quiver varieties ... provide a unified exposition enriched with numerous examples.","one_line_summary":"Unified survey linking resolutions, Hilbert schemes, McKay correspondence, and deformations for bamboo-type cyclic quotient singularities.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That independently developed results from different contexts can be unified into a single coherent exposition without introducing inconsistencies, oversimplifications, or loss of technical detail.","pith_extraction_headline":"Various independently developed results on minimal resolutions of cyclic quotient singularities unify into one coherent exposition."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.04472/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"9ad2fdf7cc5d022de69f7cd01b42372f4ef1eaba7c98bb5b6d106aed0df4452e"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}