Calabi-Yau manifolds in weighted projective spaces and their mirror gauged linear sigma models

The goal of the present paper is to calculate the complex structure moduli space Kähler potentials for hypersurfaces in weighted projective spaces and compare with the partition functions of their mirror gauged linear sigma models. We explicitly perform the Kähler potential computation and show that the corresponding formula is well defined in the case of quasismooth hypersurfaces. We then construct the mirror gauged linear sigma models with an appropriate number of Kähler 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.