{"paper":{"title":"T-Duality and Homological Mirror Symmetry of Toric Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.AG","authors_text":"Bohan Fang, Chiu-Chu Melissa Liu, David Treumann, Eric Zaslow","submitted_at":"2008-11-09T22:56:57Z","abstract_excerpt":"Let $X_\\Sigma$ be a complete toric variety. The coherent-constructible correspondence $\\kappa$ of \\cite{FLTZ} equates $\\Perf_T(X_\\Sigma)$ with a subcategory $Sh_{cc}(M_\\bR;\\LS)$ of constructible sheaves on a vector space $M_\\bR.$ The microlocalization equivalence $\\mu$ of \\cite{NZ,N} relates these sheaves to a subcategory $Fuk(T^*M_\\bR;\\LS)$ of the Fukaya category of the cotangent $T^*M_\\bR$. When $X_\\Si$ is nonsingular, taking the derived category yields an equivariant version of homological mirror symmetry, $DCoh_T(X_\\Si)\\cong DFuk(T^*M_\\bR;\\LS)$, which is an equivalence of triangulated tens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1228","kind":"arxiv","version":4},"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"}