  We apply a universal normal Calabi-Yau algebra to the construction and
classification of compact complex $n$-dimensional spaces with SU(n) holonomy
and their fibrations. This algebraic approach includes natural extensions of
reflexive weight vectors to higher dimensions and a `dual' construction based
on the Diophantine decomposition of invariant monomials. The latter provides
recurrence formulae for the numbers of fibrations of Calabi-Yau spaces in
arbitrary dimensions, which we exhibit explicitly for some Weierstrass and K3
examples.
