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Let $(X,D)$ be a pair consisting of a normal complex variety $X$ and an effective Weil divisor $D$ such that the sheaf of logarithmic vector fields (or dually the sheaf of reflexive logarithmic $1$-forms) is locally free. We prove that in this case the following holds: If $(X,D)$ is dlt, then $X$ is necessarily smooth and $\\lfloor D\\rfloor $ is snc. If $(X,D)$ is lc or the logarithmic $1$-forms are locally generated by closed forms, then $(X,\\lfloor D\\rfloor)$ is toroidal."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.04052","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-12-11T22:11:28Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"a9c0c6b30d57b54e0d2a7ce76b3026ec6aa10577493fccf843b3cee77e898a6e","abstract_canon_sha256":"580fb5b75b09a1caff41c05274e6a71a38edc552ff471bfb67be08c2c9d4c921"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:09.386657Z","signature_b64":"hPLt3UG3eJGENjGIdHaD3JDI/SGKceLkXs3/X24wlmshonp/qyFsdd7ii23XrZqaONIJZGqI0Y1Er6Xt0Z2EDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9412dc6b5b313c49c361a55043740410675bab665ba0007966c0003996874ce2","last_reissued_at":"2026-05-18T00:28:09.385820Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:09.385820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Lipman-Zariski conjecture for logarithmic vector fields on log canonical pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Hannah Bergner","submitted_at":"2017-12-11T22:11:28Z","abstract_excerpt":"We consider a version of the Lipman-Zariski conjecture for logarithmic vector fields and logarithmic $1$-forms on pairs. 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