{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:DH3VMZFOUXAU6K4S3YHU3AQUUX","short_pith_number":"pith:DH3VMZFO","schema_version":"1.0","canonical_sha256":"19f75664aea5c14f2b92de0f4d8214a5cc880f4f47d0f8557371c3366fdfaf19","source":{"kind":"arxiv","id":"1804.00463","version":2},"attestation_state":"computed","paper":{"title":"MBM loci in families of hyperkahler manifolds and centers of birational contractions","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ekaterina Amerik, Misha Verbitsky","submitted_at":"2018-04-02T11:56:24Z","abstract_excerpt":"An MBM class on a hyperkahler manifold M is a second cohomology class such that its orthogonal complement in H^2(M) contains a maximal dimensional face of the boundary of the Kahler cone for some hyperkahler deformation of M. An MBM curve is a rational curve in an MBM class and such that its local deformation space has minimal possible dimension 2n-2, where 2n is the complex dimension of M. We study the MBM loci, defined as the subvarieties covered by deformations of an MBM curve within M. When M is projective, MBM loci are centers of birational contractions. For each MBM class z, we consider "},"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":"1804.00463","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AG","submitted_at":"2018-04-02T11:56:24Z","cross_cats_sorted":[],"title_canon_sha256":"1734dc46f58216e941b0e9896ace05035bd24118ea60bc3a2659fb465241c910","abstract_canon_sha256":"7e0a3ab96b645181c7614014b2e2ca2d20eb86ee1c92684bb3b553a4bc632b42"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:09.747839Z","signature_b64":"Zu6b0ZWeybuVgerb1qUl49rVTjJM3cGZY+sabnqhX2kFTFhik0VQV+EBZcj9OW+EpQfkOTBQP6RyBpS8FiFGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19f75664aea5c14f2b92de0f4d8214a5cc880f4f47d0f8557371c3366fdfaf19","last_reissued_at":"2026-05-17T23:51:09.747299Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:09.747299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"MBM loci in families of hyperkahler manifolds and centers of birational contractions","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ekaterina Amerik, Misha Verbitsky","submitted_at":"2018-04-02T11:56:24Z","abstract_excerpt":"An MBM class on a hyperkahler manifold M is a second cohomology class such that its orthogonal complement in H^2(M) contains a maximal dimensional face of the boundary of the Kahler cone for some hyperkahler deformation of M. An MBM curve is a rational curve in an MBM class and such that its local deformation space has minimal possible dimension 2n-2, where 2n is the complex dimension of M. We study the MBM loci, defined as the subvarieties covered by deformations of an MBM curve within M. When M is projective, MBM loci are centers of birational contractions. For each MBM class z, we consider "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00463","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":"1804.00463","created_at":"2026-05-17T23:51:09.747400+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.00463v2","created_at":"2026-05-17T23:51:09.747400+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.00463","created_at":"2026-05-17T23:51:09.747400+00:00"},{"alias_kind":"pith_short_12","alias_value":"DH3VMZFOUXAU","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DH3VMZFOUXAU6K4S","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DH3VMZFO","created_at":"2026-05-18T12:32:19.392346+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/DH3VMZFOUXAU6K4S3YHU3AQUUX","json":"https://pith.science/pith/DH3VMZFOUXAU6K4S3YHU3AQUUX.json","graph_json":"https://pith.science/api/pith-number/DH3VMZFOUXAU6K4S3YHU3AQUUX/graph.json","events_json":"https://pith.science/api/pith-number/DH3VMZFOUXAU6K4S3YHU3AQUUX/events.json","paper":"https://pith.science/paper/DH3VMZFO"},"agent_actions":{"view_html":"https://pith.science/pith/DH3VMZFOUXAU6K4S3YHU3AQUUX","download_json":"https://pith.science/pith/DH3VMZFOUXAU6K4S3YHU3AQUUX.json","view_paper":"https://pith.science/paper/DH3VMZFO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.00463&json=true","fetch_graph":"https://pith.science/api/pith-number/DH3VMZFOUXAU6K4S3YHU3AQUUX/graph.json","fetch_events":"https://pith.science/api/pith-number/DH3VMZFOUXAU6K4S3YHU3AQUUX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DH3VMZFOUXAU6K4S3YHU3AQUUX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DH3VMZFOUXAU6K4S3YHU3AQUUX/action/storage_attestation","attest_author":"https://pith.science/pith/DH3VMZFOUXAU6K4S3YHU3AQUUX/action/author_attestation","sign_citation":"https://pith.science/pith/DH3VMZFOUXAU6K4S3YHU3AQUUX/action/citation_signature","submit_replication":"https://pith.science/pith/DH3VMZFOUXAU6K4S3YHU3AQUUX/action/replication_record"}},"created_at":"2026-05-17T23:51:09.747400+00:00","updated_at":"2026-05-17T23:51:09.747400+00:00"}