ScalingStacks

Conjecture 0.2 . [02YT]

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Conjecture 0.2.

The Strominger-Yau-Zaslow conjecture. If XX and Xˇ\check{X} are a mirror pair of Calabi-Yau nn-folds, then there exists fibrations f:X→Bf:X\rightarrow B and fˇ:Xˇ→B\check{f}:\check{X}\rightarrow B whose fibres are special Lagrangian, with general fibre an nn-torus. Furthermore, these fibrations are dual, in the sense that canonically Xb=H1​(Xˇb,ℝ/ℤ)X_{b}=H^{1}(\check{X}_{b},\mathbb{R}/\mathbb{Z}) and Xˇb=H1​(Xb,ℝ/ℤ)\check{X}_{b}=H^{1}(X_{b},\mathbb{R}/\mathbb{Z}) whenever XbX_{b} and Xˇb\check{X}_{b} are non-singular tori.

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