{"paper":{"title":"A basis theorem for Genus-One Conformal Blocks and modular invariance of intertwining operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.QA","authors_text":"Jianqi Liu, Xu Gao","submitted_at":"2025-08-02T10:03:39Z","abstract_excerpt":"We prove that trace functions associated to intertwining operators over a strongly rational vertex operator algebra form a global frame of the conformal block bundle $\\mathscr{C}_{\\mathbb{H}}(W)$ over $\\mathbb{H}$. Consequently, for each $\\tau\\in\\mathbb{H}$, these trace functions, evaluated at $\\tau$, form a basis of the fiber $\\mathscr{C}(E_\\tau,\\mathsf{p},z,W)$, and the natural $\\mathrm{SL}(2,\\mathbb{Z})$-action on the fiber is represented in this basis. This result is both a generalization and a refinement of Zhu's and Dong-Li-Mason's modular invariance theorems for trace functions associat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.01294","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/2508.01294/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"}