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These are curves C of degree d and genus g lying on a smooth quartic, such that (i) $4d-30 \\le g\\le 14$ or $(g,d) = (19,12)$, (ii) there is no 5-secant line, 9-secant conic, nor 13-secant twisted cubic to C. This generalises the classical similar situation for the blow-up of points in P^2.\n  We describe then Sarkisov links constructed from these blow-ups, and are able to prove the existence of Sarkisov links which were previously only known as numerical possibilities."},"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":"1106.3716","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-19T07:52:53Z","cross_cats_sorted":[],"title_canon_sha256":"10fbb38ff66d811a61abe4ea6dc2ded3ecb194110f06058df9c17101a80e4bd0","abstract_canon_sha256":"1130cf055aa1dc2ca19ddfde60832259a88830449922e7495057a5003eaa9cc3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:15.085396Z","signature_b64":"PXtInNLJmCWWDounHaQWFQOdeTbCFYLSJ34gjWJO8lK2gMXBbAxgtqOjryGB5nykk1cTxqt8eroKaWplD7c4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cee34f0d82ce18ada5a4d5f138d73ca5d4daa5893cca92c51c9d6f68d0ff3ce9","last_reissued_at":"2026-05-18T03:30:15.084579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:15.084579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak Fano threefolds obtained by blowing-up a space curve and construction of Sarkisov links","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"J\\'er\\'emy Blanc, St\\'ephane Lamy","submitted_at":"2011-06-19T07:52:53Z","abstract_excerpt":"We characterise smooth curves in P^3 whose blow-up produces a threefold with anticanonical divisor big and nef. 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