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Integral affine structures on spheres and torus fibrations of Calabi-Yau toric hypersurfaces I

Christian Haase·Ilia Zharkov
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Abstract

We describe in purely combinatorial terms dual pairs of integral affine structures on spheres which come from the conjectural metric collapse of mirror families of Calabi-Yau toric hypersurfaces. The same structures arise on the base of a special Lagrangian torus fibration in the Strominger-Yau-Zaslow conjecture. We study the topological torus fibration in the large complex structure limit and show that it coincides with our combinatorial model.

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Christian Haase, Ilia Zharkov. 2002-05-30. Integral affine structures on spheres and torus fibrations of Calabi-Yau toric hypersurfaces I. https://arxiv.org/abs/math/0205321

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