{"paper":{"title":"Flops and mutations for crepant resolutions of polyhedral singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Alvaro Nolla de Celis, Yuhi Sekiya","submitted_at":"2011-08-11T09:04:36Z","abstract_excerpt":"Let $G$ be a polyhedral group $G\\subset SO(3)$ of types $\\mathbb{Z}/n\\mathbb{Z}$, $D_{2n}$ and $\\mathbb{T}$. We prove that there exists a one-to-one correspondence between flops of $G$-Hilb$\\mathbb{C}^3$ and mutations of the McKay quiver with potential which do not mutate the trivial vertex. This correspondence provides two equivalent methods to construct every projective crepant resolution for the singularities $\\mathbb{C}^3/G$, which are constructed as moduli spaces $\\mathcal{M}_C$ of quivers with potential for some chamber $C$ in the space $\\Theta$ of stability conditions. In addition, we s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2352","kind":"arxiv","version":3},"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"}