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As an application, if $Y$ is a $n$-dimensional Fano manifold such that $-K_Y=(n-3)H$ for some ample divisor $H$, then $\\vert mH\\vert$ is basepoint free for $m\\geq 4$ and if the morphism $\\Phi_{\\vert 4H\\vert}$ is not birational onto its image, then $Y$ is either a weighted hypersurface of degree $10$ in the weighted projective space $\\mathb"},"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":"1809.00481","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-03T07:54:20Z","cross_cats_sorted":[],"title_canon_sha256":"cb2472cdad65e8526fb06d7f2d5b98353939ce78f4b66fb215018bfd3b509e8e","abstract_canon_sha256":"be0b57f4711c8bfbb13f9adc21986ac98c8fe86b095eec68bdb9254ebf02714f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:35.133786Z","signature_b64":"J9PDtg3Po5nsmyw8sAugPVSKnJ4vVMFRGFA7cRmnvgiOeIxRN/zMnv3TFMZYz8X4f1TN+b/3jCTwm2uQhZ6wAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"958bc53af78c905f7aaaae91a396d9e761ae83fb9001372a3e4787f7a5522fe1","last_reissued_at":"2026-05-18T00:06:35.133231Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:35.133231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Note on quasi-polarized canonical Calabi-Yau threefolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jie Liu","submitted_at":"2018-09-03T07:54:20Z","abstract_excerpt":"Let $(X,L)$ be a quasi-polarized canonical Calabi-Yau threefold. 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