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Let $N(X)$ be Picard lattice of $X$.\n  In math.AG/0309348 and math.AG/0606289, all divisors in moduli of $(X,H)$ (i. e. pairs $H\\in N(X)$ with $\\rk N(X)=2$) implying $M_X(v)\\cong X$ were described. They give some Mukai's correspondences of $X$ with itself.\n  Applying these results, we show that there exists $v$ and a codimension 2 submoduli in moduli of $(X,H)$ (i. e. a pair $H\\in N(X)$ with $\\rk N(X)=3$) implying $M_X(v)\\cong X$, but this submoduli ca"},"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/0609233","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2006-09-08T11:40:49Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"afe8f7880922b3c5589a9cc20495ebaf74079d55323508c09fb346ca4a40f9ab","abstract_canon_sha256":"f9e5160957645c0cfb8db881d2887dfb7eda2d65293d683600ec1ac7de0d1f89"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:32.140346Z","signature_b64":"TpMJFuDoDerSedSt5nvcUKmpFRdEPKTIpAxQabDCn4Tsi4xzwt1cn7aZfi0g/+rZWSg5O+aZrtBou/8neaA0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca3a924cdcbed2e5966190344af54b0b210c7115c3dfe9f342aa2e64f7523101","last_reissued_at":"2026-05-18T04:11:32.139750Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:32.139750Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Correspondences of a K3 surface with itself via moduli of sheaves. 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They give some Mukai's correspondences of $X$ with itself.\n  Applying these results, we show that there exists $v$ and a codimension 2 submoduli in moduli of $(X,H)$ (i. e. a pair $H\\in N(X)$ with $\\rk N(X)=3$) implying $M_X(v)\\cong X$, but this submoduli ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609233","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":"math/0609233","created_at":"2026-05-18T04:11:32.139830+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0609233v1","created_at":"2026-05-18T04:11:32.139830+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609233","created_at":"2026-05-18T04:11:32.139830+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZI5JETG4X3JO","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZI5JETG4X3JOLFTB","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZI5JETG4","created_at":"2026-05-18T12:25:54.717736+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/ZI5JETG4X3JOLFTBSA2EV5KLBM","json":"https://pith.science/pith/ZI5JETG4X3JOLFTBSA2EV5KLBM.json","graph_json":"https://pith.science/api/pith-number/ZI5JETG4X3JOLFTBSA2EV5KLBM/graph.json","events_json":"https://pith.science/api/pith-number/ZI5JETG4X3JOLFTBSA2EV5KLBM/events.json","paper":"https://pith.science/paper/ZI5JETG4"},"agent_actions":{"view_html":"https://pith.science/pith/ZI5JETG4X3JOLFTBSA2EV5KLBM","download_json":"https://pith.science/pith/ZI5JETG4X3JOLFTBSA2EV5KLBM.json","view_paper":"https://pith.science/paper/ZI5JETG4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0609233&json=true","fetch_graph":"https://pith.science/api/pith-number/ZI5JETG4X3JOLFTBSA2EV5KLBM/graph.json","fetch_events":"https://pith.science/api/pith-number/ZI5JETG4X3JOLFTBSA2EV5KLBM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZI5JETG4X3JOLFTBSA2EV5KLBM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZI5JETG4X3JOLFTBSA2EV5KLBM/action/storage_attestation","attest_author":"https://pith.science/pith/ZI5JETG4X3JOLFTBSA2EV5KLBM/action/author_attestation","sign_citation":"https://pith.science/pith/ZI5JETG4X3JOLFTBSA2EV5KLBM/action/citation_signature","submit_replication":"https://pith.science/pith/ZI5JETG4X3JOLFTBSA2EV5KLBM/action/replication_record"}},"created_at":"2026-05-18T04:11:32.139830+00:00","updated_at":"2026-05-18T04:11:32.139830+00:00"}