Special Lagrangian torus fibrations of complete intersection Calabi-Yau manifolds: a geometric conjecture

TL;DR

This paper proposes a geometric approach to constructing special Lagrangian torus fibrations on complete intersection Calabi-Yau manifolds in toric varieties, extending previous combinatorial conjectures.

Contribution

It introduces a geometric version of the Gross-Haase-Zharkov conjecture, generalizing earlier work on special Lagrangian fibrations.

Findings

Provides a geometric framework for the conjectural fibrations

Extends previous combinatorial conjectures to a geometric setting

Lays groundwork for further verification of Strominger-Yau-Zaslow predictions

Abstract

For complete intersection Calabi-Yau manifolds in toric varieties, Gross and Haase-Zharkov have given a conjectural combinatorial description of the special Lagrangian torus fibrations whose existence was predicted by Strominger, Yau and Zaslow. We present a geometric version of this construction, generalizing an earlier conjecture of the first author.