  In this note we study several conditions to be imposed on a mirror symmetry
candidate to the generic multi-quasihomogeneous Calabi-Yau variety defined in
the product of the quasihomogeneous projective spaces. We propose several
properties for a Calabi-Yau complete intersection variety so that its period
integrals can be expressed by means of quasihomogeneous weights of its mirror
symmetry candidate as it has been suggested by Berglund, Candelas et altri. As
a corollary, we see certain duality between the monodromy data and the
Poincar\'e polynomials of the Euler characteristic for the pairs of our
varieties.
