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

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

References in corpus (3)

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Amoebas of algebraic varieties
• Limiting behavior of local Calabi-Yau metrics

Cited by in corpus (4)

• SYZ conjecture for Calabi-Yau hypersurfaces in the Fermat family
• Tropical contractions to integral affine manifolds with singularities
• Special Lagrangian torus fibrations of complete intersection Calabi-Yau manifolds: a geometric conjecture
• Affine elliptic surfaces with type-A singularities and orbi-conifolds