{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:WOSHTYEGIMXXPJCZKRWNBGYMHK","short_pith_number":"pith:WOSHTYEG","schema_version":"1.0","canonical_sha256":"b3a479e086432f77a459546cd09b0c3ab8d87706bb04b6880cd7b9c2a0432f5f","source":{"kind":"arxiv","id":"1609.06827","version":3},"attestation_state":"computed","paper":{"title":"On embeddings of the Grassmannian $Gr(2,m)$ into the Grassmannian $Gr(2,n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Minhyuk Kwon","submitted_at":"2016-09-22T05:51:37Z","abstract_excerpt":"In this {paper}, we consider holomorphic embeddings of $Gr(2,m)$ into $Gr(2,n)$. We study such embeddings by finding all possible total Chern classes of the pull-back of the universal bundles under these embeddings. Using the relations between Chern classes of the universal bundles and Schubert cycles, together with properties of holomorphic vector bundles of rank $2$ on complex Grassmannians, we find conditions on $m$ and $n$ for which any holomorphic embedding of $Gr(2,m)$ into $Gr(2,n)$ is linear."},"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":"1609.06827","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-22T05:51:37Z","cross_cats_sorted":[],"title_canon_sha256":"45487b93902ef94f855efc4c2572c3ec3c3c319827762fc76e5722c7c7d1f58e","abstract_canon_sha256":"e5fec2901f19282e539dc78300802580a0b0eae1a57d46b4d920c104776497a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:42.466272Z","signature_b64":"qrBY+qVU026HWY2ytKU5pb8Tf+C9rgV7KxRav4sDVdRsZViq2+w9qVnRmAngc5ah1onILphtDH9irHyGcic1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3a479e086432f77a459546cd09b0c3ab8d87706bb04b6880cd7b9c2a0432f5f","last_reissued_at":"2026-05-18T00:50:42.465552Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:42.465552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On embeddings of the Grassmannian $Gr(2,m)$ into the Grassmannian $Gr(2,n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Minhyuk Kwon","submitted_at":"2016-09-22T05:51:37Z","abstract_excerpt":"In this {paper}, we consider holomorphic embeddings of $Gr(2,m)$ into $Gr(2,n)$. We study such embeddings by finding all possible total Chern classes of the pull-back of the universal bundles under these embeddings. Using the relations between Chern classes of the universal bundles and Schubert cycles, together with properties of holomorphic vector bundles of rank $2$ on complex Grassmannians, we find conditions on $m$ and $n$ for which any holomorphic embedding of $Gr(2,m)$ into $Gr(2,n)$ is linear."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06827","kind":"arxiv","version":3},"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":"1609.06827","created_at":"2026-05-18T00:50:42.465669+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.06827v3","created_at":"2026-05-18T00:50:42.465669+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06827","created_at":"2026-05-18T00:50:42.465669+00:00"},{"alias_kind":"pith_short_12","alias_value":"WOSHTYEGIMXX","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"WOSHTYEGIMXXPJCZ","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"WOSHTYEG","created_at":"2026-05-18T12:30:51.357362+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/WOSHTYEGIMXXPJCZKRWNBGYMHK","json":"https://pith.science/pith/WOSHTYEGIMXXPJCZKRWNBGYMHK.json","graph_json":"https://pith.science/api/pith-number/WOSHTYEGIMXXPJCZKRWNBGYMHK/graph.json","events_json":"https://pith.science/api/pith-number/WOSHTYEGIMXXPJCZKRWNBGYMHK/events.json","paper":"https://pith.science/paper/WOSHTYEG"},"agent_actions":{"view_html":"https://pith.science/pith/WOSHTYEGIMXXPJCZKRWNBGYMHK","download_json":"https://pith.science/pith/WOSHTYEGIMXXPJCZKRWNBGYMHK.json","view_paper":"https://pith.science/paper/WOSHTYEG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.06827&json=true","fetch_graph":"https://pith.science/api/pith-number/WOSHTYEGIMXXPJCZKRWNBGYMHK/graph.json","fetch_events":"https://pith.science/api/pith-number/WOSHTYEGIMXXPJCZKRWNBGYMHK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WOSHTYEGIMXXPJCZKRWNBGYMHK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WOSHTYEGIMXXPJCZKRWNBGYMHK/action/storage_attestation","attest_author":"https://pith.science/pith/WOSHTYEGIMXXPJCZKRWNBGYMHK/action/author_attestation","sign_citation":"https://pith.science/pith/WOSHTYEGIMXXPJCZKRWNBGYMHK/action/citation_signature","submit_replication":"https://pith.science/pith/WOSHTYEGIMXXPJCZKRWNBGYMHK/action/replication_record"}},"created_at":"2026-05-18T00:50:42.465669+00:00","updated_at":"2026-05-18T00:50:42.465669+00:00"}