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

TL;DR

This paper extends a combinatorial model for torus fibrations of Calabi-Yau toric hypersurfaces, exploring their connection to complex and Kähler geometry, advancing understanding of their geometric structures.

Contribution

It introduces a detailed link between the combinatorial model and the complex and Kähler geometry of Calabi-Yau hypersurfaces, building on previous work.

Findings

Established a connection between the combinatorial model and complex geometry.

Linked the model to Kähler structures of Calabi-Yau hypersurfaces.

Enhanced understanding of torus fibrations in Calabi-Yau geometry.

Abstract

This paper is a continuation of our paper math.AG/0205321 where we have built a combinatorial model for the torus fibrations of Calabi-Yau toric hypersurfaces. This part addresses the connection between the model torus fibration and the complex and K\"ahler geometry of the hypersurfaces.