If $M$ is projective and if one (and hence all) of the fibers $M_{y}$ with $y\in N\backslash f(S)$ is a torus, then as $t$ approaches zero the Ricci–flat metrics $\tilde{\omega}_{t}$ converge in $C^{\infty}_{\mathrm{loc}}(M\backslash S,\omega_{M})$ to $f^{*}\omega$, where $\omega$ is a Kähler metric on $N\backslash f(S)$ with $\Ric(\omega)=\omega_{\rm WP}$. Given any compact set $K\subset M\backslash S$ there is a constant $C_{K}$ such that the sectional curvature of $\tilde{\omega}_{t}$ satisfies

(1.2)

$$\sup_{K}|\mathrm{Sec}(\tilde{\omega}_{t})|\leqslant C_{K},$$

for all small $t>0$. Furthermore, on each torus fiber $M_{y}$ with $y\in N\backslash f(S)$ we have

(1.3)

$$\frac{\tilde{\omega}_{t}|_{M_{y}}}{t}\to\omega_{SF,y},$$

where $\omega_{SF,y}$ is the unique flat metric on $M_{y}$ cohomologous to $\omega_{M}|_{M_{y}}$ and the convergence is smooth and uniform as $y$ varies on a compact subset of $N\backslash f(S)$.