{"paper":{"title":"Rank $r$ DT theory from rank $0$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.AG","authors_text":"Richard P. Thomas, Soheyla Feyzbakhsh","submitted_at":"2021-03-04T09:42:20Z","abstract_excerpt":"Fix a Calabi-Yau 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr\\`i-Toda, such as the quintic 3-fold. We express Joyce's generalised DT invariants counting Gieseker semistable sheaves of any rank $r\\ge1$ on $X$ in terms of those counting sheaves of rank 0 and pure dimension 2.\n  The basic technique is to reduce the ranks of sheaves by replacing them by the cokernels of their Mochizuki/Joyce-Song pairs and then use wall crossing to handle their stability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.02915","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.02915/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}