{"paper":{"title":"Extended McKay correspondence for quotient surface singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Akira Ishii, Iku Nakamura","submitted_at":"2016-09-14T06:06:30Z","abstract_excerpt":"Let $G$ be a finite subgroup of $\\mbox{GL}(2)$ acting on $\\mathbf{A}^2\\setminus\\{0\\}$ freely. The $G$-orbit Hilbert scheme $G\\mbox{-Hilb}(\\mathbf{A}^2)$ is a minimal resolution of the quotient $\\mathbf{A}^2/G$. We determine the generator sheaf of the ideal defining the universal $G$-cluster over $G\\mbox{-Hilb}(\\mathbf{A}^2)$, which somewhat strengthens the well-known McKay correspondence for a finite subgroup of $\\mbox{SL}(2)$. We also study the quiver structure of $G\\mbox{-Hilb}(\\mathbf{A}^2)$ at every $G$-cluster $O_{Z_y}=O_{\\mathbf{A}^2}/I_y$ in terms of a collection of sort of minimal $G$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04143","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"}