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This Q is also the moduli space of vortices for the standard action of U(r) on {\\mathbb C}^r. The group \\text{PGL}(r, {\\mathbb C}) acts on Q via the action of $\\text{GL}(r, {\\mathbb C})$ on ${\\mathcal O}^{\\oplus r}_X$. We prove that this subgroup $\\text{PGL}(r, {\\mathbb C})$ is the connected component, containing the identity element, of the holomorphic automorphism group Aut(\\mathcal Q)"},"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":"1211.3306","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-11-14T14:04:03Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"46ed54074c02a42fa30a43b038a655546a76d0608265f30ea49f91a35e23921d","abstract_canon_sha256":"e7d7631379dac98b9a7f0a22ed4a86369c0983d862906301d8c4789b498c5876"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:50.238242Z","signature_b64":"FEmJ9MVfY11ufI7fMborixKK5CLJPDmzWXq6FK2tSqn+HwMWyWx9r9AIS6tp8Gcr7TUxvkrXQkfR1lA022utBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60f0f58c59f65c4ad08457eda937f31d8311e575c2e189696ec264d91957cce3","last_reissued_at":"2026-05-18T03:40:50.237579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:50.237579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Automorphisms of the Quot schemes associated to compact Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Ajneet Dhillon, Indranil Biswas, Jacques Hurtubise","submitted_at":"2012-11-14T14:04:03Z","abstract_excerpt":"Let X be a compact connected Riemann surface of genus at least two. Fix positive integers r and d. Let Q denote the Quot scheme that parametrizes the torsion quotients of {\\mathcal O}^{\\oplus r}_X of degree d. This Q is also the moduli space of vortices for the standard action of U(r) on {\\mathbb C}^r. The group \\text{PGL}(r, {\\mathbb C}) acts on Q via the action of $\\text{GL}(r, {\\mathbb C})$ on ${\\mathcal O}^{\\oplus r}_X$. We prove that this subgroup $\\text{PGL}(r, {\\mathbb C})$ is the connected component, containing the identity element, of the holomorphic automorphism group Aut(\\mathcal Q)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3306","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":"1211.3306","created_at":"2026-05-18T03:40:50.237687+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.3306v1","created_at":"2026-05-18T03:40:50.237687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3306","created_at":"2026-05-18T03:40:50.237687+00:00"},{"alias_kind":"pith_short_12","alias_value":"MDYPLDCZ6ZOE","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"MDYPLDCZ6ZOEVUEE","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"MDYPLDCZ","created_at":"2026-05-18T12:27:14.488303+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/MDYPLDCZ6ZOEVUEEK7W2SN7TDW","json":"https://pith.science/pith/MDYPLDCZ6ZOEVUEEK7W2SN7TDW.json","graph_json":"https://pith.science/api/pith-number/MDYPLDCZ6ZOEVUEEK7W2SN7TDW/graph.json","events_json":"https://pith.science/api/pith-number/MDYPLDCZ6ZOEVUEEK7W2SN7TDW/events.json","paper":"https://pith.science/paper/MDYPLDCZ"},"agent_actions":{"view_html":"https://pith.science/pith/MDYPLDCZ6ZOEVUEEK7W2SN7TDW","download_json":"https://pith.science/pith/MDYPLDCZ6ZOEVUEEK7W2SN7TDW.json","view_paper":"https://pith.science/paper/MDYPLDCZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.3306&json=true","fetch_graph":"https://pith.science/api/pith-number/MDYPLDCZ6ZOEVUEEK7W2SN7TDW/graph.json","fetch_events":"https://pith.science/api/pith-number/MDYPLDCZ6ZOEVUEEK7W2SN7TDW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MDYPLDCZ6ZOEVUEEK7W2SN7TDW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MDYPLDCZ6ZOEVUEEK7W2SN7TDW/action/storage_attestation","attest_author":"https://pith.science/pith/MDYPLDCZ6ZOEVUEEK7W2SN7TDW/action/author_attestation","sign_citation":"https://pith.science/pith/MDYPLDCZ6ZOEVUEEK7W2SN7TDW/action/citation_signature","submit_replication":"https://pith.science/pith/MDYPLDCZ6ZOEVUEEK7W2SN7TDW/action/replication_record"}},"created_at":"2026-05-18T03:40:50.237687+00:00","updated_at":"2026-05-18T03:40:50.237687+00:00"}