Ribbon graphs and mirror symmetry
Ribbon graphs and mirror symmetry
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带状图和镜像对称
DOI：
10.1007/s00029-014-0149-7
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
E. Zaslow
中科院分区：
文献类型：
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作者：
Nicolò Sibilla;David Treumann;E. Zaslow
给定一个具有某种额外结构的带状图$$\Gamma $$Γ，我们利用可构造层定义了一个dg范畴$$\mathrm {CPM}（\Gamma）$$CPM（Γ），用来模拟由$$\Gamma .$$描述的Teichmüller空间胞腔中黎曼曲面的福谷范畴。I.当$$\Gamma $$Γ被适当地修饰并且允许组合的“带截面的环面纤维化”时，我们从$$\Gamma $$Γ构造具有环面分量的一维代数栈$$\widetilde{X}_\Gamma $$X~Γ。我们证明了我们的模型等价于$$\mathcal {P}\mathrm {erf}（\widetilde{X}_\Gamma）$$Perf（X~Γ），即$$\widetilde{X}_\Gamma $$X~Γ上完全复形的dg范畴.
Given a ribbon graph $$\Gamma $$Γ with some extra structure, we define, using constructible sheaves, a dg category $$\mathrm {CPM}(\Gamma )$$CPM(Γ) meant to model the Fukaya category of a Riemann surface in the cell of Teichmüller space described by $$\Gamma .$$Γ. When $$\Gamma $$Γ is appropriately decorated and admits a combinatorial “torus fibration with section,” we construct from $$\Gamma $$Γ a one-dimensional algebraic stack $$\widetilde{X}_\Gamma $$X~Γ with toric components. We prove that our model is equivalent to $$\mathcal {P}\mathrm {erf}(\widetilde{X}_\Gamma )$$Perf(X~Γ), the dg category of perfect complexes on $$\widetilde{X}_\Gamma $$X~Γ.