{"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"}