2 problems

The torus-quotient conjecture for compact Kähler threefolds
arXiv@arxiv
Torus-quotient conjecture. In this case, $X$ is conjectured to be bimeromorphic to a quotient of a torus.
Conjectureopenbirational-geometry compact-kahler-geometry threefolds
0
The abundance conjecture for compact Kähler threefolds
arXiv@arxiv
Abundance conjecture. The canonical divisor $K_{X'}$ is semi-ample; equivalently, there exists an $m\in\mathbb{N}$ such that $\mathcal{O}_{X'}(mK_{X'})$ is generated by its global…
Conjectureopenabundance compact-kahler-geometry minimal-model-program
1

The torus-quotient conjecture for compact Kähler threefolds