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We prove that any rational curve on $M$ is a generalized Hecke curve. Furthermore, we study the lines on $M$, and prove that $M$ is covered by the lines when $(r, d)=r$; for the case $(r,d)<r$, the lines fill up a closed subvariety of $M$, and we determine the number of its irreducible components and th"},"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":"1305.3394","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-15T09:06:33Z","cross_cats_sorted":[],"title_canon_sha256":"64b4e43a23f0fdd253bf625275db77e40dcd42797799947b815214006dba1f14","abstract_canon_sha256":"91c25a140dcb9fa1c67c61ceb5db0945eec41c5719de7c5f815c18432ff1ffb0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:48.742207Z","signature_b64":"ud8J/GVOowGt2IRq11dx3XYjozL119U96rEH0LgILOJasBLCp3mPWx8Tazf7TPvsRSHx71n9VXEKAHriSmfTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92fc32ae26c3b3049fbd7ee79c942d286592da153fc2a5b361a1b9809923d98d","last_reissued_at":"2026-05-18T02:45:48.741620Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:48.741620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rational curves and lines on the moduli space of stable bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Mingshuo Zhou","submitted_at":"2013-05-15T09:06:33Z","abstract_excerpt":"Fix a smooth projetive curve $\\mathcal {C}$ of genus $g\\geq 2$ and a line bundle $\\mathcal{L}$ on $\\mathcal{C}$ of degree $d$. Let $M:= \\mathcal{SU}_{\\mathcal{C}}(r, \\mathcal{L})$ be the moduli space of stable vector bundles on $\\mathcal{C}$ of rank $r$ and with fixed determinant $\\mathcal{L}$. We prove that any rational curve on $M$ is a generalized Hecke curve. Furthermore, we study the lines on $M$, and prove that $M$ is covered by the lines when $(r, d)=r$; for the case $(r,d)<r$, the lines fill up a closed subvariety of $M$, and we determine the number of its irreducible components and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3394","kind":"arxiv","version":5},"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":"1305.3394","created_at":"2026-05-18T02:45:48.741703+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.3394v5","created_at":"2026-05-18T02:45:48.741703+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3394","created_at":"2026-05-18T02:45:48.741703+00:00"},{"alias_kind":"pith_short_12","alias_value":"SL6DFLRGYOZQ","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_16","alias_value":"SL6DFLRGYOZQJH55","created_at":"2026-05-18T12:27:59.945178+00:00"},{"alias_kind":"pith_short_8","alias_value":"SL6DFLRG","created_at":"2026-05-18T12:27:59.945178+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/SL6DFLRGYOZQJH55P3TZZFBNFB","json":"https://pith.science/pith/SL6DFLRGYOZQJH55P3TZZFBNFB.json","graph_json":"https://pith.science/api/pith-number/SL6DFLRGYOZQJH55P3TZZFBNFB/graph.json","events_json":"https://pith.science/api/pith-number/SL6DFLRGYOZQJH55P3TZZFBNFB/events.json","paper":"https://pith.science/paper/SL6DFLRG"},"agent_actions":{"view_html":"https://pith.science/pith/SL6DFLRGYOZQJH55P3TZZFBNFB","download_json":"https://pith.science/pith/SL6DFLRGYOZQJH55P3TZZFBNFB.json","view_paper":"https://pith.science/paper/SL6DFLRG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.3394&json=true","fetch_graph":"https://pith.science/api/pith-number/SL6DFLRGYOZQJH55P3TZZFBNFB/graph.json","fetch_events":"https://pith.science/api/pith-number/SL6DFLRGYOZQJH55P3TZZFBNFB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SL6DFLRGYOZQJH55P3TZZFBNFB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SL6DFLRGYOZQJH55P3TZZFBNFB/action/storage_attestation","attest_author":"https://pith.science/pith/SL6DFLRGYOZQJH55P3TZZFBNFB/action/author_attestation","sign_citation":"https://pith.science/pith/SL6DFLRGYOZQJH55P3TZZFBNFB/action/citation_signature","submit_replication":"https://pith.science/pith/SL6DFLRGYOZQJH55P3TZZFBNFB/action/replication_record"}},"created_at":"2026-05-18T02:45:48.741703+00:00","updated_at":"2026-05-18T02:45:48.741703+00:00"}