{"paper":{"title":"On the Quot scheme $\\mathrm{Quot}_{\\mathcal O_{\\mathbb P^1}^r/\\mathbb P^1/k}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Cristina Bertone, Margherita Roggero, Steven L. Kleiman","submitted_at":"2019-06-05T11:35:36Z","abstract_excerpt":"We consider the quot scheme $\\mathrm{Quot}^d_{\\mathcal F^r/ \\mathbb P^1/ k}$ of locally free quotients of $\\mathcal F^r:= \\bigoplus ^{ r} \\mathcal O_{\\mathbb P^1 }$ with Hilbert polynomial $p(t)=d$. We prove that it is a smooth variety of dimension $dr$, locally isomorphic to $\\mathbb A^{dr}$. We introduce a new notion of support for modules in $\\mathrm{Quot}^d_{\\mathcal F^r/ \\mathbb P^1/ k}$, called Hilb-support that allows us to define a natural surjective morphism of schemes $\\xi :\\mathrm{Quot}^d_{\\mathcal F^r/ \\mathbb P^1/ k} \\to \\mathrm{Hilb}^d_{\\mathcal O_{\\mathbb P^1}} $ associating to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01953","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"}