Integral affine structures on spheres and torus fibrations of Calabi-Yau toric hypersurfaces I
arXiv:math/0205321
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.
26 pages, 16 figures, see also http://www.duke.edu/~haase, or http://www.duke.edu/~zharkov