{"paper":{"title":"Flops and spherical functors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Agnieszka Bodzenta, Alexey Bondal","submitted_at":"2015-11-02T20:28:33Z","abstract_excerpt":"We study derived categories of Gorenstein varieties X and X^+ connected by a flop. We assume that the flopping contractions f: X \\to Y, f^+: X^+ \\to Y have fibers of dimension bounded by 1 and Y has canonical hypersurface singularities of multiplicity 2. We consider the fiber product W=X \\times_Y X^+ with projections p: W \\to X, q: W \\to X^+ and prove that the flop functors F = Rq_* Lp^*: D^b(X) \\to D^b(X^+), F^+= Rp_*Lq^*: D^b(X^+) \\to D^b(X) are equivalences, inverse to those constructed by M. Van den Bergh.\n  The composite F^+ \\circ F: D^b(X) \\to D^b(X) is a non-trivial auto-equivalence. Wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00665","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"}