Quotients of Hypersurfaces in Weighted Projective Space

In [1] some quotients of one-parameter families of Calabi-Yau varieties are related to the family of Mirror Quintics by using a construction due to Shioda. In this paper, we generalize this construction to a wider class of varieties. More specifically, let A be an invertible matrix with non-negative integer entries. We introduce varieties XA and MA in weighted projective space and in P, respectively. The variety MA turns out to be a quotient of a Fermat variety by a finite group. As a by-product, XA is a quotient of a Fermat variety and MA is a quotient of XA by a finite group. We apply this construction to some families of Calabi-Yau manifolds in order to show their birationality.