SPECIAL GEOMETRY ON CALABI-YAU MODULI SPACES AND Q -INVARIANT MILNOR RINGS

摘要

The moduli spaces of Calabi-Yau (CY) manifolds are the special K?hler manifolds. The special K?hler geometry determines the low-energy effective theory which arises in Superstring theory after the compactification on a CY manifold. For the cases, where the CY manifold is given as a hypersurface in the weighted projective space, a new procedure for computing the K?hler potential of the moduli space has been proposed by Konstantin Aleshkin and myself. The method is based on the fact that the moduli space of CY manifolds is a marginal subspace of the Frobenius manifold which arises on the deformation space of the corresponding Landau-Ginzburg superpotential. I review this approach and demonstrate its efficiency by computing the Special geometry of the 101-dimensional moduli space of the quintic threefold around the orbifold point.