Ribbon graphs and mirror symmetry

• Nicolò Sibilla ^[1] ; David Treumann ^[2] ; Eric Zaslow
  1. [1] Max Planck Institute for Mathematics

     Max Planck Institute for Mathematics

     Kreisfreie Stadt Bonn, Alemania

     
  2. [2] Boston College

     Boston College

     City of Boston, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 20, Nº. 4, 2014, págs. 979-1002
• Idioma: inglés
• DOI: 10.1007/s00029-014-0149-7
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• Resumen

  • Given a ribbon graph ΓΓ with some extra structure, we define, using constructible sheaves, a dg category CPM(Γ)CPM(Γ) meant to model the Fukaya category of a Riemann surface in the cell of Teichmüller space described by Γ.Γ. When ΓΓ is appropriately decorated and admits a combinatorial “torus fibration with section,” we construct from ΓΓ a one-dimensional algebraic stack X˜ΓX~Γ with toric components. We prove that our model is equivalent to Perf(X˜Γ)Perf(X~Γ) , the dg category of perfect complexes on X˜ΓX~Γ .