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For $0 \\leq n \\leq 9$ we calculate Okounkov bodies of graded linear series given by sections of multiples of line bundles $\\pi^\\ast \\mathcal{O}_{\\mathbb{P}^2}(d) \\otimes \\mathcal{O}_X(-m\\sum_{i=1}^n E_i)$ with respect to a flag consisting of a line on $\\mathbb{CP}^2$ and a point on the line in general position. Furthermore, we show what Nagata's Conjecture predicts on these Okounkov bodies when $n > 9$."},"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":"1409.1736","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-05T11:00:17Z","cross_cats_sorted":[],"title_canon_sha256":"511ab370b11cbec512d9d099a5e2e21d685e9071cbad959dc7c643a62d7b1bc5","abstract_canon_sha256":"54b0b2064eca8e817f472769d3a173a2f73e3e0ff7c067e4636eeb0f2b4a46a4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:38.799151Z","signature_b64":"9ZToOfJTcoVE789SOW2sZFDtBbbkGkVnAIVMreVQBbBrVFtBm3THDRoNCXfnDYE0AInjwz8PH9cYbiW7UJveBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"933ac7ff8ecc13da4b2116a4a14153e0c6c35372a2e93f0ab2766871b573b76d","last_reissued_at":"2026-05-18T02:26:38.798585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:38.798585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Iterative dissection of Okounkov bodies of graded linear series on $\\mathbb{CP}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Thomas Eckl","submitted_at":"2014-09-05T11:00:17Z","abstract_excerpt":"Let $\\pi: X \\rightarrow \\mathbb{P}^2$ be the blow-up of $\\mathbb{CP}^2$ in $n$ points $x_i$ in very general position, and let $E_i$ be the exceptional divisor over $x_i$. For $0 \\leq n \\leq 9$ we calculate Okounkov bodies of graded linear series given by sections of multiples of line bundles $\\pi^\\ast \\mathcal{O}_{\\mathbb{P}^2}(d) \\otimes \\mathcal{O}_X(-m\\sum_{i=1}^n E_i)$ with respect to a flag consisting of a line on $\\mathbb{CP}^2$ and a point on the line in general position. Furthermore, we show what Nagata's Conjecture predicts on these Okounkov bodies when $n > 9$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1736","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1409.1736","created_at":"2026-05-18T02:26:38.798681+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.1736v2","created_at":"2026-05-18T02:26:38.798681+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1736","created_at":"2026-05-18T02:26:38.798681+00:00"},{"alias_kind":"pith_short_12","alias_value":"SM5MP74OZQJ5","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SM5MP74OZQJ5USZB","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SM5MP74O","created_at":"2026-05-18T12:28:49.207871+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SM5MP74OZQJ5USZBC2SKCQKT4D","json":"https://pith.science/pith/SM5MP74OZQJ5USZBC2SKCQKT4D.json","graph_json":"https://pith.science/api/pith-number/SM5MP74OZQJ5USZBC2SKCQKT4D/graph.json","events_json":"https://pith.science/api/pith-number/SM5MP74OZQJ5USZBC2SKCQKT4D/events.json","paper":"https://pith.science/paper/SM5MP74O"},"agent_actions":{"view_html":"https://pith.science/pith/SM5MP74OZQJ5USZBC2SKCQKT4D","download_json":"https://pith.science/pith/SM5MP74OZQJ5USZBC2SKCQKT4D.json","view_paper":"https://pith.science/paper/SM5MP74O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.1736&json=true","fetch_graph":"https://pith.science/api/pith-number/SM5MP74OZQJ5USZBC2SKCQKT4D/graph.json","fetch_events":"https://pith.science/api/pith-number/SM5MP74OZQJ5USZBC2SKCQKT4D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SM5MP74OZQJ5USZBC2SKCQKT4D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SM5MP74OZQJ5USZBC2SKCQKT4D/action/storage_attestation","attest_author":"https://pith.science/pith/SM5MP74OZQJ5USZBC2SKCQKT4D/action/author_attestation","sign_citation":"https://pith.science/pith/SM5MP74OZQJ5USZBC2SKCQKT4D/action/citation_signature","submit_replication":"https://pith.science/pith/SM5MP74OZQJ5USZBC2SKCQKT4D/action/replication_record"}},"created_at":"2026-05-18T02:26:38.798681+00:00","updated_at":"2026-05-18T02:26:38.798681+00:00"}