{"paper":{"title":"Moduli of McKay quiver representations I: the coherent component","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Alastair Craw, Diane Maclagan, Rekha R. Thomas","submitted_at":"2005-05-06T19:10:52Z","abstract_excerpt":"For a finite abelian group G in GL(n,k), we describe the coherent component Y_theta of the moduli space M_theta of theta-stable McKay quiver representations. This is a not-necessarily-normal toric variety that admits a projective birational morphism to A^n/G obtained by variation of GIT quotient. As a special case, this gives a new construction of Nakamura's G-Hilbert scheme that avoids the (typically highly singular) Hilbert scheme of |G|-points in A^n. To conclude, we describe the toric fan of Y_theta and hence calculate the quiver representation corresponding to any point of Y_theta."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505115","kind":"arxiv","version":2},"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"}