The real Monge-Ampère equation governs also the region near the intersection of $X_{t}$ with a smooth component of the toric boundary. Suppose after normalising by powers of $t$, the dominant monomials are $z_{0}^{-1},z_{0}^{-1}z_{1},z_{0}^{-1}z_{2},z_{0}^{-1}z_{3},1$ in the coordinates $z_{0},z_{1},z_{2},z_{3}$ on the algebraic torus $(\mathbb{C}^{*})^{4}$, so the hypersurface has the local complex geometric model $\{z_{0}^{-1}(1+z_{1}+z_{2}+z_{3})+1=0\}\subset(\mathbb{C}^{*})^{4}$, or equivalently $-z_{0}=1+z_{1}+z_{2}+z_{3}$. The adjunction formula

$$\frac{dz_{0}}{z_{0}}\wedge\frac{dz_{1}}{z_{1}}\wedge\frac{dz_{2}}{z_{2}}\wedge\frac{dz_{3}}{z_{3}}=d(z_{0}^{-1}(1+z_{1}+z_{2}+z_{3})+1)\wedge\Omega$$

leads to $\Omega=\frac{dz_{1}}{z_{1}}\wedge\frac{dz_{2}}{z_{2}}\wedge\frac{dz_{3}}{z_{3}}$ as before. The diagonal $T^{3}$-action on $z_{1},z_{2},z_{3}$ provides the candidate for an approximate SYZ fibration, and a solution to the real Monge-Ampère equation in the $\log|z_{1}|,\log|z_{2}|,\log|z_{3}|$ coordinates induces a local Calabi-Yau metric.