6 problems

Peternell's conjecture. Any Moishezon manifold without rational curves is projective.

The fiberwise birational model conjecture. Then $g$ is fiberwise birational to a flat, projective morphism $g^{\rm p}:X^{\rm p}\to\mathbb D$ such that, respectively, $X_0^{\rm p}$…

The general-type component conjecture. Then $g$ is Moishezon, and all other fibers are of general type over a possibly smaller disc.

The rational-singularity limit conjecture. Then $X_0$ is Moishezon.

The simple normal crossing degeneration conjecture. Under these assumptions, $g$ is Moishezon.

The local Moishezon morphism criterion. The morphism $g$ is locally Moishezon if and only if every irreducible component of every fiber $X_s$ is Moishezon.