  Let M(d,n) be the moduli stack of hypersurfaces of degree d > n in the
complex projective n-space, and let M(d,n;1) be the sub-stack, parameterizing
hypersurfaces obtained as a d fold cyclic covering of the projective n-1 space,
ramified over a hypersurface of degree d. Iterating this construction, one
obtains M(d,n;r).
  We show that M(d,n;1) is rigid in M(d,n), although the Griffiths-Yukawa
coupling degenerates for d<2n. On the other hand, for all d>n the sub-stack
M(d,n;2) deforms.
  We calculate the exact length of the Griffiths-Yukawa coupling over M(d,n;r),
and we construct a 4-dimensional family of quintic hypersurfaces, and a dense
set of points in the base, where the fibres have complex multiplication.
