{"paper":{"title":"Global dimension function on stability conditions and Gepner equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Yu Qiu","submitted_at":"2018-06-29T18:00:05Z","abstract_excerpt":"We study the global dimension function $\\operatorname{gldim}\\colon\\operatorname{Aut}\\backslash\\operatorname{Stab}\\mathcal{D}/\\mathbb{C}\\to\\mathbb{R}_{\\ge0}$ on a quotient of the space of Bridgeland stability conditions on a triangulated category $\\mathcal{D}$ as well as Toda's Gepner equatio $\\Phi(\\sigma)=s\\cdot\\sigma$ for some $\\sigma\\in\\operatorname{Stab}\\mathcal{D}$ and $(\\Phi,s)\\in\\operatorname{Aut}\\mathcal{D}\\times\\mathbb{C}$.\n  For the bounded derived category $\\mathcal{D}^b(\\mathbf{k} Q)$ of a Dynkin quiver $Q$, we show that there is a unique minimal point $\\sigma_G$ of $\\operatorname{g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00010","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1807.00010/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}