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.
2014
20
4
979
1002
Sibilla, N.; Treumann, D.; Zaslow, E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/117713
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