{"paper":{"title":"Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AT"],"primary_cat":"math.DG","authors_text":"Dominic Joyce, Jacob Gross, Yalong Cao","submitted_at":"2018-11-21T13:17:23Z","abstract_excerpt":"This paper concerns orientability of moduli spaces of Spin(7)-instantons on compact 8-manifolds $X$ with Spin(7)-structure for the Lie groups SU($m$) and U($m$), and of moduli spaces of coherent sheaves on Calabi-Yau 4-folds. Such orientations are needed to define enumerative invariants 'counting' Spin(7) instantons, or coherent sheaves on Calabi-Yau 4-folds $X$. The previous version of the paper, version 2, published in Advances in Mathematics 368 (2020), claimed to prove all these moduli spaces are orientable.\n  VERSION 3 BEGINS WITH AN ERRATUM. THERE IS A MISTAKE IN THE PROOF OF THEOREM 1.1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09658","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/1811.09658/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"}