Let $\mathbb{C}^{3}$ be equipped with the holomorphic volume form $\Omega$ above, and let $\omega$ be any $T^{2}$-invariant Kähler form with infinite volume on the singular loci $\{z_{i}=z_{j}=0\}$ for any $i,j$. Then the discriminant locus of the singular $T^{2}$-bundle is $\mathfrak{D}\subset\mathbb{R}^{2}_{\mu_{1},\mu_{2}}\times\mathbb{C}_{\eta}$ in moment coordinates $\mu_{1},\mu_{2}$ and $\eta$.