{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:KWRRTG2ZLSOF4QTDM62ONYMXKW","short_pith_number":"pith:KWRRTG2Z","schema_version":"1.0","canonical_sha256":"55a3199b595c9c5e426367b4e6e1975581e01304dbfe2731fd1476408e7ef695","source":{"kind":"arxiv","id":"1906.01953","version":1},"attestation_state":"computed","paper":{"title":"On the Quot scheme $\\mathrm{Quot}_{\\mathcal O_{\\mathbb P^1}^r/\\mathbb P^1/k}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Cristina Bertone, Margherita Roggero, Steven L. Kleiman","submitted_at":"2019-06-05T11:35:36Z","abstract_excerpt":"We consider the quot scheme $\\mathrm{Quot}^d_{\\mathcal F^r/ \\mathbb P^1/ k}$ of locally free quotients of $\\mathcal F^r:= \\bigoplus ^{ r} \\mathcal O_{\\mathbb P^1 }$ with Hilbert polynomial $p(t)=d$. We prove that it is a smooth variety of dimension $dr$, locally isomorphic to $\\mathbb A^{dr}$. We introduce a new notion of support for modules in $\\mathrm{Quot}^d_{\\mathcal F^r/ \\mathbb P^1/ k}$, called Hilb-support that allows us to define a natural surjective morphism of schemes $\\xi :\\mathrm{Quot}^d_{\\mathcal F^r/ \\mathbb P^1/ k} \\to \\mathrm{Hilb}^d_{\\mathcal O_{\\mathbb P^1}} $ associating to "},"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":"1906.01953","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-06-05T11:35:36Z","cross_cats_sorted":[],"title_canon_sha256":"137a15bcc3e943b26db5c228c5088aa8d49772658e0326d2297c5fab8fd7a172","abstract_canon_sha256":"5efced82236f1289e65830019c94503b13667ec22d38d8ab57b69bbbc7b6d313"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:05.655606Z","signature_b64":"zVNGXeHUq0/0rQVBV2yUq+a1gPHKcO5wnKND5Kg+pkYhcIEb481Gm1hClezjzsHBIIou0a0NdUW0+4Xauh0DBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55a3199b595c9c5e426367b4e6e1975581e01304dbfe2731fd1476408e7ef695","last_reissued_at":"2026-05-17T23:44:05.654968Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:05.654968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Quot scheme $\\mathrm{Quot}_{\\mathcal O_{\\mathbb P^1}^r/\\mathbb P^1/k}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Cristina Bertone, Margherita Roggero, Steven L. Kleiman","submitted_at":"2019-06-05T11:35:36Z","abstract_excerpt":"We consider the quot scheme $\\mathrm{Quot}^d_{\\mathcal F^r/ \\mathbb P^1/ k}$ of locally free quotients of $\\mathcal F^r:= \\bigoplus ^{ r} \\mathcal O_{\\mathbb P^1 }$ with Hilbert polynomial $p(t)=d$. We prove that it is a smooth variety of dimension $dr$, locally isomorphic to $\\mathbb A^{dr}$. We introduce a new notion of support for modules in $\\mathrm{Quot}^d_{\\mathcal F^r/ \\mathbb P^1/ k}$, called Hilb-support that allows us to define a natural surjective morphism of schemes $\\xi :\\mathrm{Quot}^d_{\\mathcal F^r/ \\mathbb P^1/ k} \\to \\mathrm{Hilb}^d_{\\mathcal O_{\\mathbb P^1}} $ associating to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01953","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":"1906.01953","created_at":"2026-05-17T23:44:05.655068+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.01953v1","created_at":"2026-05-17T23:44:05.655068+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01953","created_at":"2026-05-17T23:44:05.655068+00:00"},{"alias_kind":"pith_short_12","alias_value":"KWRRTG2ZLSOF","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"KWRRTG2ZLSOF4QTD","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"KWRRTG2Z","created_at":"2026-05-18T12:33:21.387695+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/KWRRTG2ZLSOF4QTDM62ONYMXKW","json":"https://pith.science/pith/KWRRTG2ZLSOF4QTDM62ONYMXKW.json","graph_json":"https://pith.science/api/pith-number/KWRRTG2ZLSOF4QTDM62ONYMXKW/graph.json","events_json":"https://pith.science/api/pith-number/KWRRTG2ZLSOF4QTDM62ONYMXKW/events.json","paper":"https://pith.science/paper/KWRRTG2Z"},"agent_actions":{"view_html":"https://pith.science/pith/KWRRTG2ZLSOF4QTDM62ONYMXKW","download_json":"https://pith.science/pith/KWRRTG2ZLSOF4QTDM62ONYMXKW.json","view_paper":"https://pith.science/paper/KWRRTG2Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.01953&json=true","fetch_graph":"https://pith.science/api/pith-number/KWRRTG2ZLSOF4QTDM62ONYMXKW/graph.json","fetch_events":"https://pith.science/api/pith-number/KWRRTG2ZLSOF4QTDM62ONYMXKW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KWRRTG2ZLSOF4QTDM62ONYMXKW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KWRRTG2ZLSOF4QTDM62ONYMXKW/action/storage_attestation","attest_author":"https://pith.science/pith/KWRRTG2ZLSOF4QTDM62ONYMXKW/action/author_attestation","sign_citation":"https://pith.science/pith/KWRRTG2ZLSOF4QTDM62ONYMXKW/action/citation_signature","submit_replication":"https://pith.science/pith/KWRRTG2ZLSOF4QTDM62ONYMXKW/action/replication_record"}},"created_at":"2026-05-17T23:44:05.655068+00:00","updated_at":"2026-05-17T23:44:05.655068+00:00"}