Examples of CMCY Families of 3-manifolds and their Invariants

Abstract

In this chapter we collect all examples of CMCY -families from the previous chapters, determine the length of their Yukawa couplings and compute the Hodge numbers of their fibers. In Section 10.4 we will also give an outlook to the possible construction methods of Calabi-Yau manifolds by using other Calabi-Yau manifolds in lower dimensions and cyclic automorphism groups. We recall the definition of the length of the Yukawa coupling and its computation methods in Section 10.1. Since there are equations for the Hodge numbers of the Calabi-Yau 3-manifolds obtained from the Borcea-Voisin method, we only need to list them in Section 10.2. In Section 10.3 we need to calculate a little bit to get the Hodge numbers of Calabi-yau 3-manifolds obtained from K3 surfaces with a degree 3 automorphism and Fermat curve of degree 3.