{"paper":{"title":"Flops of G-Hilb and equivalences of derived categories by variation of GIT quotient","license":"","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Akira Ishii, Alastair Craw","submitted_at":"2002-11-22T18:28:47Z","abstract_excerpt":"For a finite subgroup G in SL(3,C), Bridgeland, King and Reid proved that the moduli space of G-clusters is a crepant resolution of the quotient C^3/G. This paper considers the moduli spaces M_\\theta, introduced by Kronheimer and further studied by Sardo Infirri, which coincide with G-Hilb for a particular choice of the GIT parameter \\theta. For G Abelian, we prove that every projective crepant resolution of C^3/G is isomorphic to M_\\theta for some parameter \\theta. The key step is the description of GIT chambers in terms of the K-theory of the moduli space via the appropriate Fourier--Mukai t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0211360","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"}