{"paper":{"title":"Quot schemes and Ricci semipositivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP"],"primary_cat":"math.DG","authors_text":"Harish Seshadri, Indranil Biswas","submitted_at":"2017-03-22T17:13:44Z","abstract_excerpt":"Let $X$ be a compact connected Riemann surface of genus at least two, and let ${\\mathcal Q}_X(r,d)$ be the quot scheme that parametrizes all the torsion coherent quotients of ${\\mathcal O}^{\\oplus r}_X$ of degree $d$. This ${\\mathcal Q}_X(r,d)$ is also a moduli space of vortices on $X$. Its geometric properties have been extensively studied. Here we prove that the anticanonical line bundle of ${\\mathcal Q}_X(r,d)$ is not nef. Equivalently, ${\\mathcal Q}_X(r,d)$ does not admit any K\\\"ahler metric whose Ricci curvature is semipositive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07753","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"}