{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:XETMQIP2ASNSTJ56AD437UAB2O","short_pith_number":"pith:XETMQIP2","schema_version":"1.0","canonical_sha256":"b926c821fa049b29a7be00f9bfd001d39424e47cc1f6d94af8d122a5358844bb","source":{"kind":"arxiv","id":"1505.06488","version":1},"attestation_state":"computed","paper":{"title":"On Varieties of Lines on Linear Sections of Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Rafael Lucas de Arruda","submitted_at":"2015-05-24T21:39:29Z","abstract_excerpt":"General linear sections of codimension 2 of the Grassmannians G(1,4) and G(1,5) appear in the classification of Fano manifolds of high index. Unlike Grassmannians, these manifolds are not homogeneous. Nevertheless, their automorphisms groups have finitely many orbits. In this work we first compute the orbits of these actions. Then we give a description of the variety of lines (under the Pl\\\"ucker embedding) passing through a fixed point in each orbit of the action. As an application we show that these Fano manifolds are not weakly 2-Fano, completing the classification of weakly 2-Fano manifold"},"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":"1505.06488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-24T21:39:29Z","cross_cats_sorted":[],"title_canon_sha256":"2c79ec27e93d9d708628ecca908b249452b3f09612f0cf2b2f29d913661a61d3","abstract_canon_sha256":"9770f5f7fecfad4e39c1a35f07cfdba543048e4271169d29ef5bfdffaef974f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:44.850913Z","signature_b64":"5NPaXze/ZOLb9ATjBCMagu42tMDGGKM9vmWhcMg4ijuhCbIe78dX7qrHwLiu0tslNIwv1v7R/wW2BaBnjuBxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b926c821fa049b29a7be00f9bfd001d39424e47cc1f6d94af8d122a5358844bb","last_reissued_at":"2026-05-18T02:03:44.850204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:44.850204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Varieties of Lines on Linear Sections of Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Rafael Lucas de Arruda","submitted_at":"2015-05-24T21:39:29Z","abstract_excerpt":"General linear sections of codimension 2 of the Grassmannians G(1,4) and G(1,5) appear in the classification of Fano manifolds of high index. Unlike Grassmannians, these manifolds are not homogeneous. Nevertheless, their automorphisms groups have finitely many orbits. In this work we first compute the orbits of these actions. Then we give a description of the variety of lines (under the Pl\\\"ucker embedding) passing through a fixed point in each orbit of the action. As an application we show that these Fano manifolds are not weakly 2-Fano, completing the classification of weakly 2-Fano manifold"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06488","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":"1505.06488","created_at":"2026-05-18T02:03:44.850305+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.06488v1","created_at":"2026-05-18T02:03:44.850305+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06488","created_at":"2026-05-18T02:03:44.850305+00:00"},{"alias_kind":"pith_short_12","alias_value":"XETMQIP2ASNS","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"XETMQIP2ASNSTJ56","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"XETMQIP2","created_at":"2026-05-18T12:29:50.041715+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.00876","citing_title":"Moduli space of genus one curves on quartic and quintic del Pezzo threefolds","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XETMQIP2ASNSTJ56AD437UAB2O","json":"https://pith.science/pith/XETMQIP2ASNSTJ56AD437UAB2O.json","graph_json":"https://pith.science/api/pith-number/XETMQIP2ASNSTJ56AD437UAB2O/graph.json","events_json":"https://pith.science/api/pith-number/XETMQIP2ASNSTJ56AD437UAB2O/events.json","paper":"https://pith.science/paper/XETMQIP2"},"agent_actions":{"view_html":"https://pith.science/pith/XETMQIP2ASNSTJ56AD437UAB2O","download_json":"https://pith.science/pith/XETMQIP2ASNSTJ56AD437UAB2O.json","view_paper":"https://pith.science/paper/XETMQIP2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.06488&json=true","fetch_graph":"https://pith.science/api/pith-number/XETMQIP2ASNSTJ56AD437UAB2O/graph.json","fetch_events":"https://pith.science/api/pith-number/XETMQIP2ASNSTJ56AD437UAB2O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XETMQIP2ASNSTJ56AD437UAB2O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XETMQIP2ASNSTJ56AD437UAB2O/action/storage_attestation","attest_author":"https://pith.science/pith/XETMQIP2ASNSTJ56AD437UAB2O/action/author_attestation","sign_citation":"https://pith.science/pith/XETMQIP2ASNSTJ56AD437UAB2O/action/citation_signature","submit_replication":"https://pith.science/pith/XETMQIP2ASNSTJ56AD437UAB2O/action/replication_record"}},"created_at":"2026-05-18T02:03:44.850305+00:00","updated_at":"2026-05-18T02:03:44.850305+00:00"}