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We show that, under a certain conditions on curvature, H^0(D,F_D\\otimes I_1I_2...I_m) lies in the image of the restriction map H^0(X,F)->H^0(D,F_D). The format of our result is inspired both by Paun's simplification of Siu's proof of invariance of plurigenera and an earlier similar result due to Demailly."},"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":"1101.2077","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-01-11T09:36:34Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"36c62d7c1e76ae6b5e122c329f8c91db5ad6dc50f5e37a5bf81a1d6cb8415148","abstract_canon_sha256":"106e00144979c185af8701b8f702b528b8e17885a64b126e9c77b9f881239741"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:28.858228Z","signature_b64":"z54KaCBqDkJ28qnSFSWXZJpRtbczVdAoVPmImM3Fxi0RGZ5pa+yl9AnPPBQgJIr8IAyKQPXP34bKCrwg77p+CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6238be663ef5e0e67950a3dede4f9298b0518ccbeddab9e36d75f2e348870f84","last_reissued_at":"2026-05-18T04:11:28.857694Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:28.857694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extensions of multiply twisted pluri-canonical forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Chen-Yu Chi, Chin-Lung Wang, Sz-Sheng Wang","submitted_at":"2011-01-11T09:36:34Z","abstract_excerpt":"Given a projective variety X, a smooth divisor D, and semipositive line bundles (L_1,h_1),,...,(L_m,h_m), we consider the \"multiply twisted pluricanonical bundle\" F:=m(K_X+D)+L_1+...+L_m on X and F_D:=mK_D+(L_1+...+L_m)|_D. Let I_j be the multiplier ideal sheaves associated to h_j, j=1,...,m. We show that, under a certain conditions on curvature, H^0(D,F_D\\otimes I_1I_2...I_m) lies in the image of the restriction map H^0(X,F)->H^0(D,F_D). 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