CY Manifolds with Locally Symmetric Moduli Spaces
Abstract
Description
There is a natural sequence of CY manifolds that are double covers of the projective g dimensional spaces ramified over 2g+2 hyperplanes. We observe that some of them are obtained as quotient of the action of the semi-direct product of g-1 copies of cyclic Z/2Z groups with the symmetric g group on the product of g-copies of hyper-elliptic curves of genus g. The quotient is a double cover of the projective g space ramified over 2g+2 hyperplanes. This construction generalizes the construction of a Kummer surface. The Kodaira-Spencer classes on the Jacobian are invariant under the action of the group. Thus they form a basis of Kodaira-Spencer classes on the CY manifold. Since the bracket of any Kodaira-Spencer classes on the Jacobian are zero, then they will be zero on the CY manifold. This implies that the moduli space of those CY manifolds is a locally symmetric space.
one reference is added and several typoes are corrected. Some changes are made in the introduction
one reference is added and several typoes are corrected. Some changes are made in the introduction