{"paper":{"title":"Blow ups of $\\mathbb{P^n}$ as quiver moduli for exceptional collections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Xuqiang Qin","submitted_at":"2018-04-23T23:20:06Z","abstract_excerpt":"Suppose $P^n_m$ is the blow up of $\\mathbb{P}^n$ at a linear subspace of dimension $m$, $\\mathcal{L}=\\{L_1,\\ldots,L_r\\}$ is a (not necessarily full) strong exceptional collection of line bundles on $P^n_m$. Let $Q$ be the quiver associated to this collection. One might wonder when is $P^n_m$ the moduli space of representations of $Q$ with dimension vector $(1,\\ldots,1)$ for a suitably chosen stability condition $\\theta$: $S\\cong M_\\theta$. In this paper, we achieve such isomorphism using $\\mathcal{L}$ of length $3$. As a result, $P^n_m$ is the moduli space of representations of a very simple q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09544","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"}