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The aim of this short note is to study the relative canonical resolution of $C$ on a rational normal scroll swept out by a $g^1_k=|L|$ with $L\\in W^1_k(C)$ general. We show that the bundle of quadrics appearing in the relative canonical resolution is unbalanced if and only if $\\rho>0$ and $(k-\\rho-\\frac{7}{2})^2-2k+\\frac{23}{4}>0$."},"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":"1505.07235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-27T09:27:11Z","cross_cats_sorted":[],"title_canon_sha256":"858f52b462c744f6a40959030d16ad52fa9a3a54f72f5c609e6020eee2a698cf","abstract_canon_sha256":"59df73dd8af15aa1bc9d764dab41013b5d2afe7c1445dc8148cf6f328aecf7bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:39.857096Z","signature_b64":"M4Q2eL9qp+0G82XrcnQaFhS5fPG5109flRv+yuTEZQNBP9xnWOwcJqDQObkEDH0nttJAtHXy8DoO8buaAQOWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04741e0feb5114877fdc6ccc876a610c41a095a6cae272c358c8dce35fc8828f","last_reissued_at":"2026-05-18T00:33:39.856311Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:39.856311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resolutions of General Canonical Curves on Rational Normal Scrolls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christian Bopp, Michael Hoff","submitted_at":"2015-05-27T09:27:11Z","abstract_excerpt":"Let $C\\subset \\mathbb{P}^{g-1}$ be a general curve of genus $g$ and let $k$ be a positive integer such that the Brill-Noether number $\\rho(g,k,1)\\geq 0$ and $g > k+1$. The aim of this short note is to study the relative canonical resolution of $C$ on a rational normal scroll swept out by a $g^1_k=|L|$ with $L\\in W^1_k(C)$ general. We show that the bundle of quadrics appearing in the relative canonical resolution is unbalanced if and only if $\\rho>0$ and $(k-\\rho-\\frac{7}{2})^2-2k+\\frac{23}{4}>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07235","kind":"arxiv","version":1},"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":"1505.07235","created_at":"2026-05-18T00:33:39.856457+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.07235v1","created_at":"2026-05-18T00:33:39.856457+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07235","created_at":"2026-05-18T00:33:39.856457+00:00"},{"alias_kind":"pith_short_12","alias_value":"AR2B4D7LKEKI","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"AR2B4D7LKEKIO764","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"AR2B4D7L","created_at":"2026-05-18T12:29:10.953037+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/AR2B4D7LKEKIO764NTGIO2TBBR","json":"https://pith.science/pith/AR2B4D7LKEKIO764NTGIO2TBBR.json","graph_json":"https://pith.science/api/pith-number/AR2B4D7LKEKIO764NTGIO2TBBR/graph.json","events_json":"https://pith.science/api/pith-number/AR2B4D7LKEKIO764NTGIO2TBBR/events.json","paper":"https://pith.science/paper/AR2B4D7L"},"agent_actions":{"view_html":"https://pith.science/pith/AR2B4D7LKEKIO764NTGIO2TBBR","download_json":"https://pith.science/pith/AR2B4D7LKEKIO764NTGIO2TBBR.json","view_paper":"https://pith.science/paper/AR2B4D7L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.07235&json=true","fetch_graph":"https://pith.science/api/pith-number/AR2B4D7LKEKIO764NTGIO2TBBR/graph.json","fetch_events":"https://pith.science/api/pith-number/AR2B4D7LKEKIO764NTGIO2TBBR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AR2B4D7LKEKIO764NTGIO2TBBR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AR2B4D7LKEKIO764NTGIO2TBBR/action/storage_attestation","attest_author":"https://pith.science/pith/AR2B4D7LKEKIO764NTGIO2TBBR/action/author_attestation","sign_citation":"https://pith.science/pith/AR2B4D7LKEKIO764NTGIO2TBBR/action/citation_signature","submit_replication":"https://pith.science/pith/AR2B4D7LKEKIO764NTGIO2TBBR/action/replication_record"}},"created_at":"2026-05-18T00:33:39.856457+00:00","updated_at":"2026-05-18T00:33:39.856457+00:00"}