lineConditionsTorsZ4 -- compute a list of possible loci for Z/4Z-Godeaux surfaces

The order of the torsion group does only depend on the choice of the line in the complete intersection of the quadratic relations $Q$ in $\mathbb{P}^{11}$. A numerical Godeaux surface $X$ with torsion group $\mathbb{Z}/4$ has two special bicanonical curves: one reducible curve of the form $D_1+D_3$, where $D_i \in |K_X + t_i|$ with a torsion element $t_i$, and a double curve $2D_2$, where $D_2 \in |K_X + t_2|$. To construct surfaces with such curves, the chosen line in $Q$ must intersect two different loci in $Q$. We choose two different components of these loci and evaluate the condition that a line through two general points is completely contained in the variety $Q$. The result is a list of pairs of ideals such that each line through two general points is completely contained in $Q$ and intersect the corresponding loci in a point.