SYZ mirror symmetry for hypertoric varieties

TL;DR

This paper constructs a SYZ mirror for hypertoric varieties by developing a Lagrangian torus fibration, applying T-duality, and resolving singularities through wall and chamber structures, advancing mirror symmetry understanding.

Contribution

It introduces a novel SYZ mirror construction for hypertoric varieties, incorporating singularity resolution via wall and chamber analysis.

Findings

Constructed a Lagrangian torus fibration on hypertoric varieties.

Developed a SYZ mirror using T-duality and open Gromov-Witten invariants.

Resolved singularities through wall and chamber structures.

Abstract

We construct a Lagrangian torus fibration on a smooth hypertoric variety and a corresponding SYZ mirror variety using $T$-duality and generating functions of open Gromov-Witten invariants. The variety is singular in general. We construct a resolution using the wall and chamber structure of the SYZ base.