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The loci $F_{\\vec{a}}(X)$ form a stratification of the Fano scheme of lines on $X$. We show that for general hypersurfaces, the $F_{\\vec{a}}(X)$ have the expected dimension and, in this case, compute the class of $\\overline{F_{\\vec{a}}(X)}$ in the Chow ring of the Grassmannian of lines in $\\ma"},"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":"1705.01972","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-04T18:42:12Z","cross_cats_sorted":[],"title_canon_sha256":"e7f35b5a92fe2d19a563a4f565fc781ea59d32481634559f7a07bdd6642c92e4","abstract_canon_sha256":"130856a8426ce649b45faf942b258a2bcba04379ff41076fbc88561c40603dbc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:00.983704Z","signature_b64":"mMWw0bAZaWjUzGw/reDTiKA/nAyiDiB0YksQnJzpb2a7NNsh27Vm5vebkhftKO9UUAH2NWAc58GVMTEAZFyOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e01fca65953fda7cdbd2dbe9dbdcf2ac37e418e19dc0024f5a14592df894716f","last_reissued_at":"2026-05-18T00:45:00.983333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:00.983333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Normal bundles of lines on hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hannah Larson","submitted_at":"2017-05-04T18:42:12Z","abstract_excerpt":"Let $X \\subset \\mathbb{P}^n$ be a smooth hypersurface. Given a sequence of integers $\\vec{a} = (a_1, \\ldots, a_{n-2})$ with $a_1 \\leq \\cdots \\leq a_{n-2}$, let $F_{\\vec{a}}(X)$ be the parameter space of lines $L$ on $X$ such that $N_{L/X} \\cong \\mathcal{O}(a_1) \\oplus \\cdots \\oplus \\mathcal{O}(a_{n-2})$. The loci $F_{\\vec{a}}(X)$ form a stratification of the Fano scheme of lines on $X$. We show that for general hypersurfaces, the $F_{\\vec{a}}(X)$ have the expected dimension and, in this case, compute the class of $\\overline{F_{\\vec{a}}(X)}$ in the Chow ring of the Grassmannian of lines in $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01972","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":"1705.01972","created_at":"2026-05-18T00:45:00.983390+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.01972v1","created_at":"2026-05-18T00:45:00.983390+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01972","created_at":"2026-05-18T00:45:00.983390+00:00"},{"alias_kind":"pith_short_12","alias_value":"4AP4UZMVH7NH","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"4AP4UZMVH7NHZW6S","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"4AP4UZMV","created_at":"2026-05-18T12:30:58.224056+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1906.10290","citing_title":"Universal degeneracy classes for vector bundles on $\\mathbb{P}^1$ bundles","ref_index":20,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4AP4UZMVH7NHZW6S3PU5XXHSVQ","json":"https://pith.science/pith/4AP4UZMVH7NHZW6S3PU5XXHSVQ.json","graph_json":"https://pith.science/api/pith-number/4AP4UZMVH7NHZW6S3PU5XXHSVQ/graph.json","events_json":"https://pith.science/api/pith-number/4AP4UZMVH7NHZW6S3PU5XXHSVQ/events.json","paper":"https://pith.science/paper/4AP4UZMV"},"agent_actions":{"view_html":"https://pith.science/pith/4AP4UZMVH7NHZW6S3PU5XXHSVQ","download_json":"https://pith.science/pith/4AP4UZMVH7NHZW6S3PU5XXHSVQ.json","view_paper":"https://pith.science/paper/4AP4UZMV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.01972&json=true","fetch_graph":"https://pith.science/api/pith-number/4AP4UZMVH7NHZW6S3PU5XXHSVQ/graph.json","fetch_events":"https://pith.science/api/pith-number/4AP4UZMVH7NHZW6S3PU5XXHSVQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4AP4UZMVH7NHZW6S3PU5XXHSVQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4AP4UZMVH7NHZW6S3PU5XXHSVQ/action/storage_attestation","attest_author":"https://pith.science/pith/4AP4UZMVH7NHZW6S3PU5XXHSVQ/action/author_attestation","sign_citation":"https://pith.science/pith/4AP4UZMVH7NHZW6S3PU5XXHSVQ/action/citation_signature","submit_replication":"https://pith.science/pith/4AP4UZMVH7NHZW6S3PU5XXHSVQ/action/replication_record"}},"created_at":"2026-05-18T00:45:00.983390+00:00","updated_at":"2026-05-18T00:45:00.983390+00:00"}