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Fix positive integers $r$ and $d$ and let ${\\mathcal Q}(r,d)$ be the Quot scheme parametrizing all torsion coherent quotients of ${\\mathcal O}^{\\oplus r}_X$ of degree $d$. We prove that ${\\mathcal Q}(r,d)$ does not admit a K\\\"ahler metric whose holomorphic bisectional curvatures are all 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":"1503.08530","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-30T04:21:33Z","cross_cats_sorted":[],"title_canon_sha256":"28ea2d02627ee3bda73a1bd4202f3106bbcc32d6a3d4a0f9e9000760a46c1700","abstract_canon_sha256":"5cbe8c8d0607a9a4350a330ab56c607a645773c3c89c7eaf1ecd99695a290e7b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:01.518639Z","signature_b64":"6xq6Tzy9fs6RqEr4ltdgbQbBeauIu6ioSWIKCuSazqPs2vkil1VTlLtvvT80sm7koVO6fGjlZ5VDmog8VcUtDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3e4aad33a4637251ece54308bb4ae158f00142f69571ba1d625668335e09077","last_reissued_at":"2026-05-18T02:20:01.518068Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:01.518068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the K\\\"ahler structures over Quot schemes, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Harish Seshadri, Indranil Biswas","submitted_at":"2015-03-30T04:21:33Z","abstract_excerpt":"Let $X$ be a compact connected Riemann surface of genus $g$, with $g \\geq 2$, and let ${\\mathcal O}_X$ denote the sheaf of holomorphic functions on $X$. Fix positive integers $r$ and $d$ and let ${\\mathcal Q}(r,d)$ be the Quot scheme parametrizing all torsion coherent quotients of ${\\mathcal O}^{\\oplus r}_X$ of degree $d$. We prove that ${\\mathcal Q}(r,d)$ does not admit a K\\\"ahler metric whose holomorphic bisectional curvatures are all nonnegative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08530","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":"1503.08530","created_at":"2026-05-18T02:20:01.518178+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.08530v1","created_at":"2026-05-18T02:20:01.518178+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08530","created_at":"2026-05-18T02:20:01.518178+00:00"},{"alias_kind":"pith_short_12","alias_value":"6PSKVUZ2IY3S","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6PSKVUZ2IY3SKHWO","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6PSKVUZ2","created_at":"2026-05-18T12:29:07.941421+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/6PSKVUZ2IY3SKHWOKQYIXNFOCW","json":"https://pith.science/pith/6PSKVUZ2IY3SKHWOKQYIXNFOCW.json","graph_json":"https://pith.science/api/pith-number/6PSKVUZ2IY3SKHWOKQYIXNFOCW/graph.json","events_json":"https://pith.science/api/pith-number/6PSKVUZ2IY3SKHWOKQYIXNFOCW/events.json","paper":"https://pith.science/paper/6PSKVUZ2"},"agent_actions":{"view_html":"https://pith.science/pith/6PSKVUZ2IY3SKHWOKQYIXNFOCW","download_json":"https://pith.science/pith/6PSKVUZ2IY3SKHWOKQYIXNFOCW.json","view_paper":"https://pith.science/paper/6PSKVUZ2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.08530&json=true","fetch_graph":"https://pith.science/api/pith-number/6PSKVUZ2IY3SKHWOKQYIXNFOCW/graph.json","fetch_events":"https://pith.science/api/pith-number/6PSKVUZ2IY3SKHWOKQYIXNFOCW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6PSKVUZ2IY3SKHWOKQYIXNFOCW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6PSKVUZ2IY3SKHWOKQYIXNFOCW/action/storage_attestation","attest_author":"https://pith.science/pith/6PSKVUZ2IY3SKHWOKQYIXNFOCW/action/author_attestation","sign_citation":"https://pith.science/pith/6PSKVUZ2IY3SKHWOKQYIXNFOCW/action/citation_signature","submit_replication":"https://pith.science/pith/6PSKVUZ2IY3SKHWOKQYIXNFOCW/action/replication_record"}},"created_at":"2026-05-18T02:20:01.518178+00:00","updated_at":"2026-05-18T02:20:01.518178+00:00"}