The Polarization Longchuanhe Moduli Space Basic Building

In this paper we make a comprehensive summarization of professional docu-ments about the construction and basic properties of polarized CY manifolds.From the complex structure to Calabi-yau manifolds,we give detailed descriptions of the properties of Calabi-yau manifolds.The Teichmuller space of CY manifolds together with a universal family of marked CY manifolds exists and it has finite number of irreducible components. Each component is a non-singular com-plex manifold. The coarse moduli space of polarized CY manifolds is a quasi-projective variety and it has a finite cover space which is non-singular quasi-projective variety.There is a family of polarized CY manifolds over the cover space.The construction of the cover space and the family over it is based on the existence of family of CY manifolds over the Hilbert schemes.