{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:NUZDCGDUITDGKNFJML6CNP5MAG","short_pith_number":"pith:NUZDCGDU","schema_version":"1.0","canonical_sha256":"6d3231187444c66534a962fc26bfac01ac66400931a11a44a87679d564cea42e","source":{"kind":"arxiv","id":"2106.13287","version":2},"attestation_state":"computed","paper":{"title":"A special Debarre-Voisin fourfold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jieao Song","submitted_at":"2021-06-24T19:29:50Z","abstract_excerpt":"Consider the finite simple group $\\mathbf{G}:=\\mathrm{PSL}(2,\\mathbf{F}_{11})$ of order 660, which has an irreducible representation $V_{10}$ of dimension 10. In this note, we study a special trivector ${\\sigma_0}\\in \\bigwedge^3V_{10}^\\vee$ that is $\\mathbf{G}$-invariant. Following the construction of Debarre-Voisin, we obtain a smooth hyperk\\\"ahler fourfold $X_6^{\\sigma_0}\\subset\\mathrm{Gr}(6,V_{10})$ with many symmetries. We will also look at the associated Peskine variety $X_1^{\\sigma_0}\\subset \\mathbf{P}(V_{10})$, which is highly symmetric as well and admits 55 isolated singular points. It"},"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":"2106.13287","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-06-24T19:29:50Z","cross_cats_sorted":[],"title_canon_sha256":"2ddfefd928a735ec3bd556c7681dd30937fb0449afb3d11fad5d80cedf06dbb5","abstract_canon_sha256":"4e76c0d5650b2b14ba2f109cc2f2a2acb17b9a9a70e532ed77d64dc8f7a2ca64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:09:09.496190Z","signature_b64":"4Ub6HzLt7hlIt9Tj39Yj9oRuYJii2Vjkg8Hc49n0h17pjUwmEcmOQFKXp99MbWJksLAW19hcWfqxRTrRZgHiAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d3231187444c66534a962fc26bfac01ac66400931a11a44a87679d564cea42e","last_reissued_at":"2026-06-10T01:09:09.495058Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:09:09.495058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A special Debarre-Voisin fourfold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jieao Song","submitted_at":"2021-06-24T19:29:50Z","abstract_excerpt":"Consider the finite simple group $\\mathbf{G}:=\\mathrm{PSL}(2,\\mathbf{F}_{11})$ of order 660, which has an irreducible representation $V_{10}$ of dimension 10. In this note, we study a special trivector ${\\sigma_0}\\in \\bigwedge^3V_{10}^\\vee$ that is $\\mathbf{G}$-invariant. Following the construction of Debarre-Voisin, we obtain a smooth hyperk\\\"ahler fourfold $X_6^{\\sigma_0}\\subset\\mathrm{Gr}(6,V_{10})$ with many symmetries. We will also look at the associated Peskine variety $X_1^{\\sigma_0}\\subset \\mathbf{P}(V_{10})$, which is highly symmetric as well and admits 55 isolated singular points. It"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.13287","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.13287/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":"2106.13287","created_at":"2026-06-10T01:09:09.495221+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.13287v2","created_at":"2026-06-10T01:09:09.495221+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.13287","created_at":"2026-06-10T01:09:09.495221+00:00"},{"alias_kind":"pith_short_12","alias_value":"NUZDCGDUITDG","created_at":"2026-06-10T01:09:09.495221+00:00"},{"alias_kind":"pith_short_16","alias_value":"NUZDCGDUITDGKNFJ","created_at":"2026-06-10T01:09:09.495221+00:00"},{"alias_kind":"pith_short_8","alias_value":"NUZDCGDU","created_at":"2026-06-10T01:09:09.495221+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/NUZDCGDUITDGKNFJML6CNP5MAG","json":"https://pith.science/pith/NUZDCGDUITDGKNFJML6CNP5MAG.json","graph_json":"https://pith.science/api/pith-number/NUZDCGDUITDGKNFJML6CNP5MAG/graph.json","events_json":"https://pith.science/api/pith-number/NUZDCGDUITDGKNFJML6CNP5MAG/events.json","paper":"https://pith.science/paper/NUZDCGDU"},"agent_actions":{"view_html":"https://pith.science/pith/NUZDCGDUITDGKNFJML6CNP5MAG","download_json":"https://pith.science/pith/NUZDCGDUITDGKNFJML6CNP5MAG.json","view_paper":"https://pith.science/paper/NUZDCGDU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.13287&json=true","fetch_graph":"https://pith.science/api/pith-number/NUZDCGDUITDGKNFJML6CNP5MAG/graph.json","fetch_events":"https://pith.science/api/pith-number/NUZDCGDUITDGKNFJML6CNP5MAG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NUZDCGDUITDGKNFJML6CNP5MAG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NUZDCGDUITDGKNFJML6CNP5MAG/action/storage_attestation","attest_author":"https://pith.science/pith/NUZDCGDUITDGKNFJML6CNP5MAG/action/author_attestation","sign_citation":"https://pith.science/pith/NUZDCGDUITDGKNFJML6CNP5MAG/action/citation_signature","submit_replication":"https://pith.science/pith/NUZDCGDUITDGKNFJML6CNP5MAG/action/replication_record"}},"created_at":"2026-06-10T01:09:09.495221+00:00","updated_at":"2026-06-10T01:09:09.495221+00:00"}