Given a ribbon graph Γ with some extra structure, we define, using constructible sheaves, a dg category CPM(Γ) meant to model the Fukaya category of a Riemann surface in the cell of Teichmüller space described by Γ. When Γ is appropriately decorated and admits a combinatorial “torus fibration with section,” we construct from Γ a one-dimensional algebraic stack XΓ with toric components. We prove that our model is equivalent to Perf(XΓ), the dg category of perfect complexes on XΓ.
Ribbon graphs and mirror symmetry / Sibilla, N.; Treumann, D.; Zaslow, E.. - In: SELECTA MATHEMATICA. - ISSN 1022-1824. - 20:4(2014), pp. 979-1002. [10.1007/s00029-014-0149-7]
Ribbon graphs and mirror symmetry
Sibilla N.
;
2014-01-01
Abstract
Given a ribbon graph Γ with some extra structure, we define, using constructible sheaves, a dg category CPM(Γ) meant to model the Fukaya category of a Riemann surface in the cell of Teichmüller space described by Γ. When Γ is appropriately decorated and admits a combinatorial “torus fibration with section,” we construct from Γ a one-dimensional algebraic stack XΓ with toric components. We prove that our model is equivalent to Perf(XΓ), the dg category of perfect complexes on XΓ.| File | Dimensione | Formato | |
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