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Let I_C be the ideal sheaf of a non-hyperelliptic, genus g, canonical curve. The first conjecture states that, if g\\geq 8, and if the Clifford index of C is greater than 2, then H^1(P^{g-1}, I_C^2(k))=0, for k\\geq 3. We prove this conjecture for g\\geq 11. The second conjecture states that a Brill-Noether-Petri curve of genus g\\geq 12 "},"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":"1507.05002","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-17T15:54:55Z","cross_cats_sorted":[],"title_canon_sha256":"fdd90eaa72cae4e04149edd30fcda91cc92080d267d09031dd3c2f045a7575e2","abstract_canon_sha256":"e9ce93dfc4f9348377f870dd28ac348f0c00e313aac3f04c8d9a00cd5260a663"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:26.630955Z","signature_b64":"rk7chh3ib0VvKFRkEf8D4LV3a0Vt7mZjnphRc9qZvpACcF3Cypm8vDsCI0C1ETGjOVEyoEv+QkGgLOl0WcYcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf202aabf4d139e738a9f538b92c71d595e4e4e76c22b17d5ccaa9ae7f3a9233","last_reissued_at":"2026-05-18T00:59:26.630380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:26.630380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On hyperplane sections of K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrea Bruno, Edoardo Sernesi, Enrico Arbarello","submitted_at":"2015-07-17T15:54:55Z","abstract_excerpt":"Let C be a Brill-Noether-Petri curve of genus g\\geq 12. We prove that C lies on a polarized K3 surface, or on a limit thereof, if and only if the Gauss-Wahl map for C is not surjective. The proof is obtained by studying the validity of two conjectures by J. Wahl. Let I_C be the ideal sheaf of a non-hyperelliptic, genus g, canonical curve. The first conjecture states that, if g\\geq 8, and if the Clifford index of C is greater than 2, then H^1(P^{g-1}, I_C^2(k))=0, for k\\geq 3. We prove this conjecture for g\\geq 11. The second conjecture states that a Brill-Noether-Petri curve of genus g\\geq 12 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05002","kind":"arxiv","version":3},"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":"1507.05002","created_at":"2026-05-18T00:59:26.630475+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.05002v3","created_at":"2026-05-18T00:59:26.630475+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05002","created_at":"2026-05-18T00:59:26.630475+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z4QCVK7U2E46","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z4QCVK7U2E46OOFJ","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z4QCVK7U","created_at":"2026-05-18T12:29:52.810259+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/Z4QCVK7U2E46OOFJ6U4LSLDR2W","json":"https://pith.science/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W.json","graph_json":"https://pith.science/api/pith-number/Z4QCVK7U2E46OOFJ6U4LSLDR2W/graph.json","events_json":"https://pith.science/api/pith-number/Z4QCVK7U2E46OOFJ6U4LSLDR2W/events.json","paper":"https://pith.science/paper/Z4QCVK7U"},"agent_actions":{"view_html":"https://pith.science/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W","download_json":"https://pith.science/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W.json","view_paper":"https://pith.science/paper/Z4QCVK7U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.05002&json=true","fetch_graph":"https://pith.science/api/pith-number/Z4QCVK7U2E46OOFJ6U4LSLDR2W/graph.json","fetch_events":"https://pith.science/api/pith-number/Z4QCVK7U2E46OOFJ6U4LSLDR2W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W/action/storage_attestation","attest_author":"https://pith.science/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W/action/author_attestation","sign_citation":"https://pith.science/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W/action/citation_signature","submit_replication":"https://pith.science/pith/Z4QCVK7U2E46OOFJ6U4LSLDR2W/action/replication_record"}},"created_at":"2026-05-18T00:59:26.630475+00:00","updated_at":"2026-05-18T00:59:26.630475+00:00"}