{"paper":{"title":"Diagonal property of the symmetric product of a smooth curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Indranil Biswas, Sanjay Kumar Singh","submitted_at":"2015-02-26T16:36:25Z","abstract_excerpt":"Let $C$ be an irreducible smooth projective curve defined over an algebraically closed field. We prove that the symmetric product ${\\rm Sym}^d(C)$ has the diagonal property for all $d \\geq 1$. For any positive integers $n$ and $r$, let ${\\mathcal Q}_{{\\mathcal O}^{\\oplus n}_C}(nr)$ be the Quot scheme parametrizing all the torsion quotients of ${\\mathcal O}^{\\oplus n}_C$ of degree $nr$. We prove that ${\\mathcal Q}_{{\\mathcal O}^{\\oplus n}_C}(nr)$ has the weak point property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07626","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"}