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We prove that an indecomposable abelian variety $X$ is the Jacobian of a curve if and only if there exists a point $a=2b\\in X\\setminus\\{0\\}$ such that $<a>$ is irreducible and $\\kappa(b)$ is a flex of $\\kappa(X)$."},"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":"math/0502138","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2005-02-07T17:16:21Z","cross_cats_sorted":[],"title_canon_sha256":"be7489cd0a5d4b32314427bfb2d261e385ae5cdf6ddd13d7f680b913574d575c","abstract_canon_sha256":"a4898cef7263fd3f59b21419dbb726bc39ac52300bd2ba9b729679c8ba5f87d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:49.141791Z","signature_b64":"QW+e/jdIUGGRRW/TQG7OUE5n7/BIKqxYOH6RrDvJ/Qv7RGNjRta8ogteY97vlszORK2dBCTUTRAehj2bqo58Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"828bb864c8c1ff2b469ffa9d23757d7534636e5d07b7d5361a095b85428466fe","last_reissued_at":"2026-05-18T01:20:49.141388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:49.141388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizing Jacobians via flexes of the Kummer variety","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"E. Arbarello, G. Marini, I. Krichever","submitted_at":"2005-02-07T17:16:21Z","abstract_excerpt":"Given an abelian variety $X$ and a point $a\\in X$ we denote by $<a>$ the closure of the subgroup of $X$ generated by $a$. Let $N=2^g-1$. We denote by $\\kappa: X\\to \\kappa(X)\\subset\\mathbb P^N$ the map from $X$ to its Kummer variety. We prove that an indecomposable abelian variety $X$ is the Jacobian of a curve if and only if there exists a point $a=2b\\in X\\setminus\\{0\\}$ such that $<a>$ is irreducible and $\\kappa(b)$ is a flex of $\\kappa(X)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0502138","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":"math/0502138","created_at":"2026-05-18T01:20:49.141448+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0502138v2","created_at":"2026-05-18T01:20:49.141448+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0502138","created_at":"2026-05-18T01:20:49.141448+00:00"},{"alias_kind":"pith_short_12","alias_value":"QKF3QZGIYH7S","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"QKF3QZGIYH7SWRU7","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"QKF3QZGI","created_at":"2026-05-18T12:25:53.335082+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/QKF3QZGIYH7SWRU77KOSG5L5OU","json":"https://pith.science/pith/QKF3QZGIYH7SWRU77KOSG5L5OU.json","graph_json":"https://pith.science/api/pith-number/QKF3QZGIYH7SWRU77KOSG5L5OU/graph.json","events_json":"https://pith.science/api/pith-number/QKF3QZGIYH7SWRU77KOSG5L5OU/events.json","paper":"https://pith.science/paper/QKF3QZGI"},"agent_actions":{"view_html":"https://pith.science/pith/QKF3QZGIYH7SWRU77KOSG5L5OU","download_json":"https://pith.science/pith/QKF3QZGIYH7SWRU77KOSG5L5OU.json","view_paper":"https://pith.science/paper/QKF3QZGI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0502138&json=true","fetch_graph":"https://pith.science/api/pith-number/QKF3QZGIYH7SWRU77KOSG5L5OU/graph.json","fetch_events":"https://pith.science/api/pith-number/QKF3QZGIYH7SWRU77KOSG5L5OU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QKF3QZGIYH7SWRU77KOSG5L5OU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QKF3QZGIYH7SWRU77KOSG5L5OU/action/storage_attestation","attest_author":"https://pith.science/pith/QKF3QZGIYH7SWRU77KOSG5L5OU/action/author_attestation","sign_citation":"https://pith.science/pith/QKF3QZGIYH7SWRU77KOSG5L5OU/action/citation_signature","submit_replication":"https://pith.science/pith/QKF3QZGIYH7SWRU77KOSG5L5OU/action/replication_record"}},"created_at":"2026-05-18T01:20:49.141448+00:00","updated_at":"2026-05-18T01:20:49.141448+00:00"}