Calabi–Yau moduli space metric for hypersurfaces in weighted projective spaces

It is known that the Lagrangian of massless fields in superstring theories compactified on a Calabi–Yau 3-fold can be computed in terms the Special geometry on the CY moduli space. It is the reason why we need to know the Weil-Peterson metric on the CY moduli space. For the case where the CY is given by a hypersurface in a weighted projective space there are only few explicit computations of this metric. I will talk about a new method to compute the moduli space metric in the case of hypersurfaces in weighted projective spaces using a connection with the invariant Frobenius ring structure of the corresponding Landau–Ginzburg model. In the talk I will explain this method and illustrate its efficiency for the case 101 moduli space of the quintic threefold.