3 problems

Let $S$ be a semi-log-canonical (s.l.c.) sextic surface lying in any boundary divisor of the closure $\overline{M}^{\operatorname{sextic}}$ of the Gieseker moduli stack of sextic s…

Wormhole conjecture. The MMP on the new W-surface finishes in a minimal model and requires only flips; that is, both punctured W-surfaces live in the same moduli space.

Wormhole conjecture. The MMP requires only flips and gives a minimal model. The KSBA replacement of $(X'\subset\mathcal{X}')\to(0\in\mathbb{D})$ lives on the same moduli space as t…