{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:IBSHMLMIKYD43XYGQZEFAUBGEH","short_pith_number":"pith:IBSHMLMI","schema_version":"1.0","canonical_sha256":"4064762d885607cddf06864850502621cd401ba1443ef46cea1220f4487fa866","source":{"kind":"arxiv","id":"1904.11071","version":1},"attestation_state":"computed","paper":{"title":"Biquadratic addition laws on elliptic curves in $\\mathbb{P}^3$ and the canonical map of the $(1,2,2)$-Theta divisor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luca Cesarano","submitted_at":"2019-04-24T21:11:01Z","abstract_excerpt":"We recall that a smooth ample surface $\\mathcal{S}$ in a general $(1,2,2)$-polarized abelian threefold, which is the pullback of the Theta divisor of a smooth plane quartic curve $\\mathcal{D}$, is a surface isogenous to the product $\\mathcal{C} \\times \\mathcal{C}$, where $\\mathcal{C}$ is a genus $9$ curve embedded in $\\mathbb{P}^3$ as complete intersection of a smooth quadric and a smooth quartic. We show that the space of global holomorhic sections of the canonical bundle of this surface is generated by certain determinantal bihomogeneous polynomials of bidegree $(2,2)$ on $\\mathbb{P}^3$, whi"},"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":"1904.11071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-04-24T21:11:01Z","cross_cats_sorted":[],"title_canon_sha256":"fa5e672d8a98327592ad57470c11389853a6153707ede2d2bbb5280e5c6d3a25","abstract_canon_sha256":"58466b004f43cf87da701f29a67bf1c71c9a7992a1c7e3f63b2549650a65f7a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:45.902713Z","signature_b64":"I3+dJjedOqbQFSmiJ9JUmZraoDWBeSmeSWbCV6FTIBT7BTFGSSGnp8ZqsduPjSQ9zSvSK7EBJKcQ+Zzux9DIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4064762d885607cddf06864850502621cd401ba1443ef46cea1220f4487fa866","last_reissued_at":"2026-05-17T23:47:45.902171Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:45.902171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Biquadratic addition laws on elliptic curves in $\\mathbb{P}^3$ and the canonical map of the $(1,2,2)$-Theta divisor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luca Cesarano","submitted_at":"2019-04-24T21:11:01Z","abstract_excerpt":"We recall that a smooth ample surface $\\mathcal{S}$ in a general $(1,2,2)$-polarized abelian threefold, which is the pullback of the Theta divisor of a smooth plane quartic curve $\\mathcal{D}$, is a surface isogenous to the product $\\mathcal{C} \\times \\mathcal{C}$, where $\\mathcal{C}$ is a genus $9$ curve embedded in $\\mathbb{P}^3$ as complete intersection of a smooth quadric and a smooth quartic. We show that the space of global holomorhic sections of the canonical bundle of this surface is generated by certain determinantal bihomogeneous polynomials of bidegree $(2,2)$ on $\\mathbb{P}^3$, whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11071","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":"1904.11071","created_at":"2026-05-17T23:47:45.902251+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.11071v1","created_at":"2026-05-17T23:47:45.902251+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11071","created_at":"2026-05-17T23:47:45.902251+00:00"},{"alias_kind":"pith_short_12","alias_value":"IBSHMLMIKYD4","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"IBSHMLMIKYD43XYG","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"IBSHMLMI","created_at":"2026-05-18T12:33:18.533446+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/IBSHMLMIKYD43XYGQZEFAUBGEH","json":"https://pith.science/pith/IBSHMLMIKYD43XYGQZEFAUBGEH.json","graph_json":"https://pith.science/api/pith-number/IBSHMLMIKYD43XYGQZEFAUBGEH/graph.json","events_json":"https://pith.science/api/pith-number/IBSHMLMIKYD43XYGQZEFAUBGEH/events.json","paper":"https://pith.science/paper/IBSHMLMI"},"agent_actions":{"view_html":"https://pith.science/pith/IBSHMLMIKYD43XYGQZEFAUBGEH","download_json":"https://pith.science/pith/IBSHMLMIKYD43XYGQZEFAUBGEH.json","view_paper":"https://pith.science/paper/IBSHMLMI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.11071&json=true","fetch_graph":"https://pith.science/api/pith-number/IBSHMLMIKYD43XYGQZEFAUBGEH/graph.json","fetch_events":"https://pith.science/api/pith-number/IBSHMLMIKYD43XYGQZEFAUBGEH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IBSHMLMIKYD43XYGQZEFAUBGEH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IBSHMLMIKYD43XYGQZEFAUBGEH/action/storage_attestation","attest_author":"https://pith.science/pith/IBSHMLMIKYD43XYGQZEFAUBGEH/action/author_attestation","sign_citation":"https://pith.science/pith/IBSHMLMIKYD43XYGQZEFAUBGEH/action/citation_signature","submit_replication":"https://pith.science/pith/IBSHMLMIKYD43XYGQZEFAUBGEH/action/replication_record"}},"created_at":"2026-05-17T23:47:45.902251+00:00","updated_at":"2026-05-17T23:47:45.902251+00:00"}