{"paper":{"title":"The Coherent-Constructible Correspondence for Toric Deligne-Mumford Stacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Bohan Fang, Chiu-Chu Melissa Liu, David Treumann, Eric Zaslow","submitted_at":"2009-11-24T20:34:46Z","abstract_excerpt":"We extend our previous work arXiv:1007.0053 on coherent-constructible correspondence for toric varieties to include toric Deligne-Mumford (DM) stacks. Following Borisov-Chen-Smith, a toric DM stack $\\cX_\\bSi$ is described by a \"stacky fan\" $\\bSi=(N,\\Si,\\beta)$, where $N$ is a finitely generated abelian group and $\\Si$ is a simplicial fan in $N_\\bR=N\\otimes_{\\bZ}\\bR$. From $\\bSi$ we define a conical Lagrangian $\\Lambda_\\bSi$ inside the cotangent $T^*M_\\bR$ of the dual vector space $M_\\bR$ of $N_\\bR$, such that torus-equivariant, coherent sheaves on $\\cX_\\bSi$ are equivalent to constructible she"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4711","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"}