The natural projection $f_{0}:\tilde{X}\longrightarrow\bar{S}^{\perp}$ is equivariant under the $\Gamma$ actions on $\tilde{X}$ and $\bar{S}^{\perp}$. For any $y\in\bar{S}^{\perp}$, $f_{0}^{-1}(y)=\tilde{S}\times\{y\}$, and $f_{0}$ is a special lagrangian fibration on $(\tilde{X},\pi^{*}\omega_{0},e^{\sqrt{-1}\theta_{0}}\pi^{*}\Omega_{0})$, i.e. $\dim_{\mathbb{R}}f_{0}^{-1}(y)=n$,