4 problems

The terminal-singularity conjecture. If the singularity $\mathbb{C}^n/G$ is terminal, then

Let $Y$ be the unit cotangent bundle of a hyperbolic surface, and let $(M=\Sigma \times Y,\xi_k)$ be the corresponding $5$-dimensional contact manifold from Corollary … have untwis…

Let $Y$ be the unit cotangent bundle of a hyperbolic surface, and let $(M=\Sigma\times Y,\xi_k)$ be the corresponding $5$-dimensional contact manifold of Theorem 5d. These examples…

Algebraic torsion conjecture. Then $(V,\xi)$ has algebraic $1$-torsion, and it is also algebraically overtwisted if $N$ contains any blown down boundary components.