{"paper":{"title":"Brauer Groups of Quot Schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ajneet Dhillon, Indranil Biswas, Jacques Hurtubise","submitted_at":"2012-12-10T14:46:37Z","abstract_excerpt":"Let $X$ be an irreducible smooth complex projective curve. Let ${\\mathcal Q}(r,d)$ be the Quot scheme parametrizing all coherent subsheaves of ${\\mathcal O}^{\\oplus r}_X$ of rank $r$ and degree $-d$. There are natural morphisms ${\\mathcal Q}(r,d) \\longrightarrow \\text{Sym}^d(X)$ and $\\text{Sym}^d(X) \\longrightarrow \\text{Pic}^d(X)$. We prove that both these morphisms induce isomorphism of Brauer groups if $d \\geq 2$. Consequently, the Brauer group of ${\\mathcal Q}(r,d)$ is identified with the Brauer group of $\\text{Pic}^d(X)$ if $d \\geq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2081","kind":"arxiv","version":2},"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"}