Find the Picard Fuchs operator of a four parameter fundamental period

Question

In my research, we have constructed a Calabi-Yau as a hypersurface of a toric variety and we could compute the fundamental period of the complex moduli, which is a series in four parameters. Say \begin{equation} \varpi_0=1+\sum_{i,j,k,l}a_{ijkl} ~z_1^i z_2^j z_3^k z_4^l \end{equation} We want to compute the Picard Fuchs operator, $\mathcal{L}$ which is a differential operator such that \begin{equation} \mathcal{L}\varpi_0=0 \end{equation}

But since there are four parameters, my computer could not find one, does anyone know any systematical way to construct such operators in four parameters? Any reference would be greatly appreciated.

Answer 1

The standard strategy would be to apply the GKZ method or the Griffiths-Dwork technique, as outlined in Cox and Katz's Mirror Symmetry and Algebraic Geometry. Is there a reason neither of these is applicable to your case?