{"paper":{"title":"Non-Equivalence of Smooth and Nodal Conformal Block Functors in Logarithmic CFT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","math.RT"],"primary_cat":"math.QA","authors_text":"Hao Zhang","submitted_at":"2025-09-09T13:20:15Z","abstract_excerpt":"Let $\\mathbb V$ be an $\\mathbb N$-graded, $C_2$-cofinite vertex operator algebra (VOA) admitting a non-lowest generated module in $\\mathrm{Mod}(\\mathbb V)$ (e.g., the triplet algebras $\\mathcal{W}_p$ for $p\\in \\mathbb{Z}_{\\geq 2}$ or the even symplectic fermion VOAs $SF_d^+$ for $d\\in \\mathbb{Z}_+$). We prove that, unlike in the rational case, the spaces of conformal blocks associated to certain $\\mathbb V$-modules do not form a vector bundle on $\\overline{\\mathcal{M}}_{0,N}$ for $N\\geq 4$ by showing that their dimensions differ between nodal and smooth curves. Consequently, the sheaf of coinv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07720","kind":"arxiv","version":1},"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/2509.07720/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"}