Ribbon graphs and mirror symmetry |
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Authors: | Nicolò Sibilla David Treumann Eric Zaslow |
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Institution: | 1. Max Planck Institute for Mathematics, Vivatsgasse 7, 53111?, Bonn, Germany 2. Department of Mathematics, Boston College, Carney Hall, Chestnut Hill, MA, 02467-3806, USA 3. Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL?, 60208, USA
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Abstract: | Given a ribbon graph \(\Gamma \) with some extra structure, we define, using constructible sheaves, a dg category \(\mathrm {CPM}(\Gamma )\) meant to model the Fukaya category of a Riemann surface in the cell of Teichmüller 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 \(\mathcal {P}\mathrm {erf}(\widetilde{X}_\Gamma )\) , the dg category of perfect complexes on \(\widetilde{X}_\Gamma \) . |
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