{"paper":{"title":"Kasteleyn operators from mirror symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.SG"],"primary_cat":"math.AG","authors_text":"David Treumann, Eric Zaslow, Harold Williams","submitted_at":"2018-10-14T07:08:22Z","abstract_excerpt":"Given a consistent bipartite graph $\\Gamma$ in $T^2$ with a complex-valued edge weighting $\\mathcal{E}$ we show the following two constructions are the same. The first is to form the Kasteleyn operator of $(\\Gamma, \\mathcal{E})$ and pass to its spectral transform, a coherent sheaf supported on a spectral curve in $(\\mathbb{C}^\\times)^2$. The second is to form the conjugate Lagrangian $L \\subset T^* T^2$ of $\\Gamma$, equip it with a brane structure prescribed by $\\mathcal{E}$, and pass to its mirror coherent sheaf. This lives on a stacky toric compactification of $(\\mathbb{C}^\\times)^2$ determi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05985","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"}