{"paper":{"title":"Stability Conditions and Exceptional Objects in Triangulated Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Zihong Chen","submitted_at":"2018-09-27T05:09:38Z","abstract_excerpt":"The goal of this paper is to study the subspace of stability condition $\\Sigma_{\\mathcal{E}}\\subset \\mathrm{Stab}(X)$ associated to an exceptional collection $\\mathcal{E}$ on a projective variety $X$. Following Emanuele Macr\\`{i}'s approach, we show a certain correspondence between the homotopy class of continuous loops in $\\Sigma_{\\mathcal{E}}$ and words of the braid group. In particular, we prove that in the case $X=\\mathbb{P}^3$ and $\\mathcal{E}=\\{\\mathcal{O},\\mathcal{O}(1),\\mathcal{O}(2),\\mathcal{O}(3)\\}$, the space $\\Sigma_{\\mathcal{E}}$ is a connected and simply connected 4-dimensional m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10344","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"}