  We construct families of Calabi-Yau manifolds with dense set of complex
multiplication fibers in an arbitrary dimension. We will also give explicite
examples of complex multiplication fibers. For this construction we use
families of curves with dense set of complex multiplication fibers. In
addition, we give examples of such families for each genus less or equal 7 and
we study the generic Hodge groups of families of cyclic covers of the
projective line.
