{"paper":{"title":"Ribbon Graphs and Mirror Symmetry I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.SG"],"primary_cat":"math.AT","authors_text":"David Treumann, Eric Zaslow, Nicol\\'o Sibilla","submitted_at":"2011-03-12T17:09:56Z","abstract_excerpt":"Given a ribbon graph $\\Gamma$ with some extra structure, we define, using constructible sheaves, a dg category $CPM(\\Gamma)$ meant to model the Fukaya category of a Riemann surface in the cell of Teichm\\\"uller space described by $\\Gamma.$ When $\\Gamma$ is appropriately decorated and admits a combinatorial \"torus fibration with section,\" we construct from $\\Gamma$ a one-dimensional algebraic stack $\\widetilde{X}_\\Gamma$ with toric components. We prove that our model is equivalent to $Perf(\\widetilde{X}_\\Gamma)$, the dg category of perfect complexes on $\\widetilde{X}_\\Gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2462","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"}