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Let ${\\mathcal Q}_X(r,n)$ be the Quot scheme parametrizing the torsion quotients of ${\\mathcal O}^{\\oplus r}_X$ of degree $n$. If $g \\geq 2$ and $n \\leq 2g-2$, we prove that ${\\mathcal Q}_X(r,n)$ does not admit a K\\\"ahler structure such that all the holomorphic bisectional curvatures are nonnegative."},"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":"1401.7408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-01-29T03:46:19Z","cross_cats_sorted":[],"title_canon_sha256":"c663b79d5bf5290b8b2ee135a9e3f3ab2081230e91134e8d9b0573f468cfd371","abstract_canon_sha256":"b5d32bc9adf8c406ae4d639fa562db3b976895e32c6d060a17aae38bae668af0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:48.572196Z","signature_b64":"ibSjACrwJkOkQSnYwQ6Gq7WB8EwLfqAo0FjTunBMSxW5I23+OSxdrz70SYY5goBrKh1qH5MgiFYnqHfe+S+uBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f47a9d28dde1b3a3b445ff8eeafe51525a422dd680fbe01c3ad16371898f6dad","last_reissued_at":"2026-05-18T03:00:48.571520Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:48.571520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the K\\\"ahler structures over Quot schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Harish Seshadri, Indranil Biswas","submitted_at":"2014-01-29T03:46:19Z","abstract_excerpt":"Let $S^n(X)$ be the $n$-fold symmetric product of a compact connected Riemann surface $X$ of genus $g$ and gonality $d$. We prove that $S^n(X)$ admits a K\\\"ahler structure such that all the holomorphic bisectional curvatures are nonpositive if and only if $n < d$. Let ${\\mathcal Q}_X(r,n)$ be the Quot scheme parametrizing the torsion quotients of ${\\mathcal O}^{\\oplus r}_X$ of degree $n$. If $g \\geq 2$ and $n \\leq 2g-2$, we prove that ${\\mathcal Q}_X(r,n)$ does not admit a K\\\"ahler structure such that all the holomorphic bisectional curvatures are nonnegative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7408","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":"1401.7408","created_at":"2026-05-18T03:00:48.571618+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.7408v1","created_at":"2026-05-18T03:00:48.571618+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7408","created_at":"2026-05-18T03:00:48.571618+00:00"},{"alias_kind":"pith_short_12","alias_value":"6R5J2KG54GZ2","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6R5J2KG54GZ2HNCF","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6R5J2KG5","created_at":"2026-05-18T12:28:16.859392+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/6R5J2KG54GZ2HNCF76HOV7SRKJ","json":"https://pith.science/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ.json","graph_json":"https://pith.science/api/pith-number/6R5J2KG54GZ2HNCF76HOV7SRKJ/graph.json","events_json":"https://pith.science/api/pith-number/6R5J2KG54GZ2HNCF76HOV7SRKJ/events.json","paper":"https://pith.science/paper/6R5J2KG5"},"agent_actions":{"view_html":"https://pith.science/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ","download_json":"https://pith.science/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ.json","view_paper":"https://pith.science/paper/6R5J2KG5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.7408&json=true","fetch_graph":"https://pith.science/api/pith-number/6R5J2KG54GZ2HNCF76HOV7SRKJ/graph.json","fetch_events":"https://pith.science/api/pith-number/6R5J2KG54GZ2HNCF76HOV7SRKJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ/action/storage_attestation","attest_author":"https://pith.science/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ/action/author_attestation","sign_citation":"https://pith.science/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ/action/citation_signature","submit_replication":"https://pith.science/pith/6R5J2KG54GZ2HNCF76HOV7SRKJ/action/replication_record"}},"created_at":"2026-05-18T03:00:48.571618+00:00","updated_at":"2026-05-18T03:00:48.571618+00:00"}