Lagrangian torus fibration of quintic Calabi-Yau hypersurfaces I: Fermat quintic case

TL;DR

This paper constructs a Lagrangian torus fibration for Fermat quintic Calabi-Yau hypersurfaces using gradient flow, analyzes monodromy, and discusses singular fiber structures, advancing understanding of mirror symmetry.

Contribution

It introduces a novel gradient flow method to construct Lagrangian torus fibrations for Fermat quintic Calabi-Yau hypersurfaces and analyzes their monodromy and singular fibers.

Findings

Constructed Lagrangian torus fibration for Fermat quintic hypersurfaces.

Computed monodromy of the fibration.

Discussed the structure of singular fibers.

Abstract

In this paper we give a construction of Lagrangian torus fibration for Fermat type quintic \cy hypersurfaces via the method of gradient flow. We also compute the monodromy of the expected special Lagrangian torus fibration and discuss structures of singular fibers.