4 problems

Xiao–Reid's Morsification conjecture. A fiber germ $f^{-1}(p)$ is atomic if and only if it is a stable curve with one node or a multiple of a smooth curve.

Reduced-fiber-free slope equality conjecture. The slope equality

Xiao–Reid's Morsification conjecture. There exists a moduli stack $\mathcal{M}^{\star}_{g}$ of curves which contains all good smoothable curves of genus $g$ as geometric points suc…

Tan–Tu conjecture. Every semistable non-isotrivial fibered surface $f:X\to \mathbb{P}^1$ of general type has at least $7$ singular fibers.