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One can also formulate it in terms of graded linear series as follows: let $W_{\\bullet} = \\{W_k \\}$ be the complete graded linear series associated to a big divisor $D$: \\[\n  W_k = H^0\\big(X,\\mathcal{O}_X(kD)\\big). \\] For each fixed positive integer $p$, define $W^{(p)}_{\\bullet}$ to be the graded linear subseries of $W_{\\bullet}$ generated by $W_p"},"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":"1005.0432","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-05-04T03:47:25Z","cross_cats_sorted":[],"title_canon_sha256":"4167014995a125f7ee919e67cc8bc1f14a42da604f4062727b2a46ece9a761fc","abstract_canon_sha256":"a8c00289e59ee3394cf751b7e84941eccbd8709f0ef8762eea913cfec4d79c5c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:09.543445Z","signature_b64":"l0TXdmycWeW/0Vzcjjvw0Nl5aDL8UIHN4F4sdUuCe4OUsIYbly8xhKPIl4SB94wBMT+IZtU/KAUIqzjAUSqXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39e4e8e735232db88a5efc6f56476a0d2cf09a7e098dd63f1fe1119e4dd1516c","last_reissued_at":"2026-05-18T04:32:09.543035Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:09.543035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multigraded Fujita Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Shin-Yao Jow","submitted_at":"2010-05-04T03:47:25Z","abstract_excerpt":"The original Fujita approximation theorem states that the volume of a big divisor $D$ on a projective variety $X$ can always be approximated arbitrarily closely by the self-intersection number of an ample divisor on a birational modification of $X$. 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