{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VCNWBPYOPQHNUFBKA3ZVULU7VC","short_pith_number":"pith:VCNWBPYO","schema_version":"1.0","canonical_sha256":"a89b60bf0e7c0eda142a06f35a2e9fa8b8b02f47be1eff7b70d09137c6b2cc1e","source":{"kind":"arxiv","id":"1812.00706","version":1},"attestation_state":"computed","paper":{"title":"Quot schemes, Segre invariants, and inflectional loci of scrolls over curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"George H. Hitching","submitted_at":"2018-12-03T12:25:12Z","abstract_excerpt":"Let $E$ be a vector bundle over a smooth curve $C$, and $S = \\mathbb{P} E$ the associated projective bundle. We describe the inflectional loci of certain projective models $\\psi \\colon S \\dashrightarrow \\mathbb{P}^n$ in terms of Quot schemes of $E$. This gives a geometric characterisation of the Segre invariant $s_1 (E)$, which leads to new geometric criteria for semistability and cohomological stability of bundles over $C$. We also use these ideas to show that for general enough $S$ and $\\psi$, the inflectional loci are all of the expected dimension. An auxiliary result, valid for a general s"},"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":"1812.00706","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-03T12:25:12Z","cross_cats_sorted":[],"title_canon_sha256":"9b9114307d90b3ecdc2ce48fa863634d0804bd6130dcc5e645f1ef5237461737","abstract_canon_sha256":"6a8a798f3c1973bc1725c8583fef7e4477b592f965fc19dbec4e42c95f6273b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:19.209251Z","signature_b64":"bNMy/FSku0MRf/hF4I5wI/0d8qScc9xnQLDMqe/54thhl1TC8r0v7h+x3PDJwKgUPI6kBX5tNBfbK/aCCLnSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a89b60bf0e7c0eda142a06f35a2e9fa8b8b02f47be1eff7b70d09137c6b2cc1e","last_reissued_at":"2026-05-17T23:59:19.208830Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:19.208830Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quot schemes, Segre invariants, and inflectional loci of scrolls over curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"George H. Hitching","submitted_at":"2018-12-03T12:25:12Z","abstract_excerpt":"Let $E$ be a vector bundle over a smooth curve $C$, and $S = \\mathbb{P} E$ the associated projective bundle. We describe the inflectional loci of certain projective models $\\psi \\colon S \\dashrightarrow \\mathbb{P}^n$ in terms of Quot schemes of $E$. This gives a geometric characterisation of the Segre invariant $s_1 (E)$, which leads to new geometric criteria for semistability and cohomological stability of bundles over $C$. We also use these ideas to show that for general enough $S$ and $\\psi$, the inflectional loci are all of the expected dimension. An auxiliary result, valid for a general s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00706","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":"1812.00706","created_at":"2026-05-17T23:59:19.208901+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.00706v1","created_at":"2026-05-17T23:59:19.208901+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00706","created_at":"2026-05-17T23:59:19.208901+00:00"},{"alias_kind":"pith_short_12","alias_value":"VCNWBPYOPQHN","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VCNWBPYOPQHNUFBK","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VCNWBPYO","created_at":"2026-05-18T12:32:59.047623+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/VCNWBPYOPQHNUFBKA3ZVULU7VC","json":"https://pith.science/pith/VCNWBPYOPQHNUFBKA3ZVULU7VC.json","graph_json":"https://pith.science/api/pith-number/VCNWBPYOPQHNUFBKA3ZVULU7VC/graph.json","events_json":"https://pith.science/api/pith-number/VCNWBPYOPQHNUFBKA3ZVULU7VC/events.json","paper":"https://pith.science/paper/VCNWBPYO"},"agent_actions":{"view_html":"https://pith.science/pith/VCNWBPYOPQHNUFBKA3ZVULU7VC","download_json":"https://pith.science/pith/VCNWBPYOPQHNUFBKA3ZVULU7VC.json","view_paper":"https://pith.science/paper/VCNWBPYO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.00706&json=true","fetch_graph":"https://pith.science/api/pith-number/VCNWBPYOPQHNUFBKA3ZVULU7VC/graph.json","fetch_events":"https://pith.science/api/pith-number/VCNWBPYOPQHNUFBKA3ZVULU7VC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VCNWBPYOPQHNUFBKA3ZVULU7VC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VCNWBPYOPQHNUFBKA3ZVULU7VC/action/storage_attestation","attest_author":"https://pith.science/pith/VCNWBPYOPQHNUFBKA3ZVULU7VC/action/author_attestation","sign_citation":"https://pith.science/pith/VCNWBPYOPQHNUFBKA3ZVULU7VC/action/citation_signature","submit_replication":"https://pith.science/pith/VCNWBPYOPQHNUFBKA3ZVULU7VC/action/replication_record"}},"created_at":"2026-05-17T23:59:19.208901+00:00","updated_at":"2026-05-17T23:59:19.208901+00:00"}