{"paper":{"title":"Orientation data for moduli spaces of coherent sheaves over Calabi-Yau 3-folds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dominic Joyce, Markus Upmeier","submitted_at":"2020-01-01T00:01:01Z","abstract_excerpt":"Let $X$ be a compact Calabi-Yau 3-fold, and write $\\mathcal M,\\bar{\\mathcal M}$ for the moduli stacks of objects in coh$(X),D^b$coh$(X)$. There are natural line bundles $K_{\\mathcal M}\\to\\mathcal M$, $K_{\\bar{\\mathcal M}}\\to\\bar{\\mathcal M}$, analogues of canonical bundles. Orientation data on $\\mathcal M,\\bar{\\mathcal M}$ is an isomorphism class of square root line bundles $K_{\\mathcal M}^{1/2},K_{\\bar{\\mathcal M}}^{1/2}$, satisfying a compatibility condition on the stack of short exact sequences. It was introduced by Kontsevich and Soibelman arXiv:1006.270 in their theory of motivic Donaldso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.00113","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.00113/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"}