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

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

2002-05-30

arxiv.org/abs/math/0205321v1

Mathematics

Algebraic Geometry

26 pages, 16 figures, see also http://www.duke.edu/~haase, or http://www.duke.edu/~zharkov

Scientific paper

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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