8 problems

$-1$-curves conjecture. The Mori cone of $S$ is generated by the light cone and the $-1$-curves. Dually,

Mori cone generation conjecture. The Mori cone $M$ of $X_\psi$ is generated by the classes of the curves $\ell_{\mathbf{t}}$, $\sigma_{\mathbf{s},\mathbf{t}}$, and…

Let $X$ be the blowup of $\mathbb{P}^2$ at $n$ sufficiently general points, and let $\mathcal{Q}_n$ and $\Delta_n^{\preccurlyeq}$ be as defined in the source. Strong Delta-conjectu…

Let $X$ be the blowup of $\mathbb{P}^2$ at $n$ sufficiently general points. Let $\mathcal{Q}_n$ be the nonnegative cone and let $\Delta_n^{\preccurlyeq}$ be the cone defined in the…

Boundedness conjecture. Let $Y$ be an irreducible holomorphic symplectic manifold birational to $X$. The set

Numerical-dimension conjecture. If

Interior-of-the-Mori-cone conjecture. The class $[C]$ lies in the interior of

Let $(X,g)$ be a polarized variety deformation equivalent to a four-dimensional generalized Kummer variety. Let $(R,R)$ denote the Beauville–Bogomolov form on homology. The general…