Optimal bound for singularities on Fano type fibrations of relative dimension one

Bingyi Chen

Let $\ddot{I}€:X\to Z$ be a Fano type fibration with $\dim X-\dim Z=d$ and let $(X,B)$ be an $\hat{I}\mu$-lc pair with $K_X+B\sim_{\RR} 0/Z$. The canonical bundle formula gives $(Z,B_Z+M_…