{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:E74UP5E7SLYLKFYH5T2PVFMGPB","short_pith_number":"pith:E74UP5E7","schema_version":"1.0","canonical_sha256":"27f947f49f92f0b51707ecf4fa9586787339ae1317918f317b1199ebe20eebf6","source":{"kind":"arxiv","id":"2608.08680","version":1},"attestation_state":"computed","paper":{"title":"A Torelli-type theorem for hyperk\\\"{a}hler quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Ryota Kotani","submitted_at":"2026-08-09T12:53:21Z","abstract_excerpt":"In this paper, we investigate the moduli space of algebraic asymptotic hyperk\\\"ahler structures on hyperk\\\"ahler quotients arising from a quaternionic vector space $\\mathbb{H}^n$. We consider the period map on this moduli space, and prove a Torelli-type theorem (i.e., the bijectivity of the period map) assuming the surjectivity of the Kirwan map. This work provides an algebro-geometric generalization of the Torelli-type theorem for ALE gravitational instantons by Kronheimer (1989). In particular, this theorem applies to toric hyperk\\\"ahler varieties and Nakajima quiver varieties."},"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":"2608.08680","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-08-09T12:53:21Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"12db74049b8c2abd13ac79c93568a3cd9b16009b097fbb610dceb9b5be90fbf6","abstract_canon_sha256":"bb478087929e3189ccaf7ffcadd8a2cf51fd5a571230456117027773d7bfed36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T01:23:27.854909Z","signature_b64":"1X18g4rpvZgvoPpl65/aIg6Fs+BCfpaN9Wt3aOL1U7j6g49JIz7oJy30RzonMkwcnQRzi6TARxYxmYEmCuM/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27f947f49f92f0b51707ecf4fa9586787339ae1317918f317b1199ebe20eebf6","last_reissued_at":"2026-08-11T01:23:27.852157Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T01:23:27.852157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Torelli-type theorem for hyperk\\\"{a}hler quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Ryota Kotani","submitted_at":"2026-08-09T12:53:21Z","abstract_excerpt":"In this paper, we investigate the moduli space of algebraic asymptotic hyperk\\\"ahler structures on hyperk\\\"ahler quotients arising from a quaternionic vector space $\\mathbb{H}^n$. We consider the period map on this moduli space, and prove a Torelli-type theorem (i.e., the bijectivity of the period map) assuming the surjectivity of the Kirwan map. This work provides an algebro-geometric generalization of the Torelli-type theorem for ALE gravitational instantons by Kronheimer (1989). In particular, this theorem applies to toric hyperk\\\"ahler varieties and Nakajima quiver varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08680","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.08680/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2608.08680","created_at":"2026-08-11T01:23:27.853259+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.08680v1","created_at":"2026-08-11T01:23:27.853259+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.08680","created_at":"2026-08-11T01:23:27.853259+00:00"},{"alias_kind":"pith_short_12","alias_value":"E74UP5E7SLYL","created_at":"2026-08-11T01:23:27.853259+00:00"},{"alias_kind":"pith_short_16","alias_value":"E74UP5E7SLYLKFYH","created_at":"2026-08-11T01:23:27.853259+00:00"},{"alias_kind":"pith_short_8","alias_value":"E74UP5E7","created_at":"2026-08-11T01:23:27.853259+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/E74UP5E7SLYLKFYH5T2PVFMGPB","json":"https://pith.science/pith/E74UP5E7SLYLKFYH5T2PVFMGPB.json","graph_json":"https://pith.science/api/pith-number/E74UP5E7SLYLKFYH5T2PVFMGPB/graph.json","events_json":"https://pith.science/api/pith-number/E74UP5E7SLYLKFYH5T2PVFMGPB/events.json","paper":"https://pith.science/paper/E74UP5E7"},"agent_actions":{"view_html":"https://pith.science/pith/E74UP5E7SLYLKFYH5T2PVFMGPB","download_json":"https://pith.science/pith/E74UP5E7SLYLKFYH5T2PVFMGPB.json","view_paper":"https://pith.science/paper/E74UP5E7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.08680&json=true","fetch_graph":"https://pith.science/api/pith-number/E74UP5E7SLYLKFYH5T2PVFMGPB/graph.json","fetch_events":"https://pith.science/api/pith-number/E74UP5E7SLYLKFYH5T2PVFMGPB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E74UP5E7SLYLKFYH5T2PVFMGPB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E74UP5E7SLYLKFYH5T2PVFMGPB/action/storage_attestation","attest_author":"https://pith.science/pith/E74UP5E7SLYLKFYH5T2PVFMGPB/action/author_attestation","sign_citation":"https://pith.science/pith/E74UP5E7SLYLKFYH5T2PVFMGPB/action/citation_signature","submit_replication":"https://pith.science/pith/E74UP5E7SLYLKFYH5T2PVFMGPB/action/replication_record"}},"created_at":"2026-08-11T01:23:27.853259+00:00","updated_at":"2026-08-11T01:23:27.853259+00:00"}