Abstract
In [Bini, van Geemen, Kelly, Mirror quintics, discrete symmetries and Shioda maps, 2009] 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 
in weighted projective space and in 
, respectively. The variety 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 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.
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