On Calabi-Yau manifolds in weighted projective spaces and their mirror GLSMs

TL;DR

This paper computes the K"ahler potential for hypersurfaces in weighted projective spaces and compares it with mirror GLSM partition functions, elucidating aspects of mirror symmetry and the structure of moduli spaces.

Contribution

It explicitly calculates the K"ahler potential for hypersurfaces in weighted projective spaces and relates it to mirror GLSM partition functions, advancing understanding of mirror symmetry.

Findings

K"ahler potential is well-defined for quasismooth hypersurfaces

Partition functions relate to different charts of the moduli space

Constructed mirror GLSM with appropriate K"ahler parameters

Abstract

The goal of the present paper is to calculate the complex structure moduli space K\"ahler potentials for hypersurfaces in weighted projective spaces and compare with the partition functions of their mirror GLSMs. We explicitly perform the K\"ahler potential computation and show that the corresponding formula is well-defined in case of quasismooth hypersurfaces. We then construct the mirror GLSM with an appropriate number of K\"ahler parameters and discuss the interpretation of its partition function in terms of mirror symmetry. Namely, it is shown that different contributions to the partition function are related to various charts of the complex structure moduli space.