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

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.