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We prove that the Gaussian map $\\Phi_{\\omega_C(-T)}$ is non-surjective, where $T$ is the degree two divisor over the singular point $x$ of $f(C)$. This generalizes a result of Kemeny with an entirely different proof. It uses the very ampleness of $C$ on the blown-up surface $\\widetilde S$ of $S$ at $x$ and a theorem of L'vovski."},"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":"1802.01311","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-02-05T09:35:45Z","cross_cats_sorted":[],"title_canon_sha256":"eca184d7d687e9c0972b55cfa62113d9a2844a3217a175771d1212a62c0779fd","abstract_canon_sha256":"e9a92f95da7a5f755fb400c4c07202bedc99c325484ce32734354229550e7153"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:28.168182Z","signature_b64":"C5+/ifLSKiIqGPK/U4jDmxBW4lNvhHLDBCVaDz+7hWWWFtSPg86ZeZHwquGVLkz0WGeDC8eW0rrv3k4WP5Q2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d629ea66cf748a6853ccefa7276f8f16a52da29331451ecef36f57e531020880","last_reissued_at":"2026-05-18T00:15:28.167496Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:28.167496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-surjective Gaussian maps for singular curves on K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Claudio Fontanari, Edoardo Sernesi","submitted_at":"2018-02-05T09:35:45Z","abstract_excerpt":"Let $(S,L)$ be a polarized K3 surface with $\\mathrm{Pic}(S) = \\mathbb{Z}[L]$ and $L\\cdot L=2g-2$, let $C$ be a nonsingular curve of genus $g-1$ and let $f:C\\to S$ be such that $f(C) \\in \\vert L \\vert$. We prove that the Gaussian map $\\Phi_{\\omega_C(-T)}$ is non-surjective, where $T$ is the degree two divisor over the singular point $x$ of $f(C)$. This generalizes a result of Kemeny with an entirely different proof. It uses the very ampleness of $C$ on the blown-up surface $\\widetilde S$ of $S$ at $x$ and a theorem of L'vovski."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01311","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":"1802.01311","created_at":"2026-05-18T00:15:28.167597+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.01311v2","created_at":"2026-05-18T00:15:28.167597+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01311","created_at":"2026-05-18T00:15:28.167597+00:00"},{"alias_kind":"pith_short_12","alias_value":"2YU6UZWPOSFG","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2YU6UZWPOSFGQU6M","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2YU6UZWP","created_at":"2026-05-18T12:32:02.567920+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/2YU6UZWPOSFGQU6M56TSO34PC2","json":"https://pith.science/pith/2YU6UZWPOSFGQU6M56TSO34PC2.json","graph_json":"https://pith.science/api/pith-number/2YU6UZWPOSFGQU6M56TSO34PC2/graph.json","events_json":"https://pith.science/api/pith-number/2YU6UZWPOSFGQU6M56TSO34PC2/events.json","paper":"https://pith.science/paper/2YU6UZWP"},"agent_actions":{"view_html":"https://pith.science/pith/2YU6UZWPOSFGQU6M56TSO34PC2","download_json":"https://pith.science/pith/2YU6UZWPOSFGQU6M56TSO34PC2.json","view_paper":"https://pith.science/paper/2YU6UZWP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.01311&json=true","fetch_graph":"https://pith.science/api/pith-number/2YU6UZWPOSFGQU6M56TSO34PC2/graph.json","fetch_events":"https://pith.science/api/pith-number/2YU6UZWPOSFGQU6M56TSO34PC2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2YU6UZWPOSFGQU6M56TSO34PC2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2YU6UZWPOSFGQU6M56TSO34PC2/action/storage_attestation","attest_author":"https://pith.science/pith/2YU6UZWPOSFGQU6M56TSO34PC2/action/author_attestation","sign_citation":"https://pith.science/pith/2YU6UZWPOSFGQU6M56TSO34PC2/action/citation_signature","submit_replication":"https://pith.science/pith/2YU6UZWPOSFGQU6M56TSO34PC2/action/replication_record"}},"created_at":"2026-05-18T00:15:28.167597+00:00","updated_at":"2026-05-18T00:15:28.167597+00:00"}