4 problems

Let $(F,g)$ be a polarized irreducible holomorphic symplectic fourfold deformation equivalent to $S^{[2]}$, and let $E^*_{\mathrm{nod}}$ be the classes corresponding to the extrema…

Let $X$ be a four-dimensional projective variety with only terminal singularities. Recall that a $\mathbb{Q}$-Cartier divisor is quasi-numerically positive if it is nef and has pos…

Fourfold Strong Conjecture remaining-case statement. This is the only unsettled case of the Strong Conjecture in dimension $4$ over $\mathbb{C}$. The claim identifies, rather than…

Let $(F,g)$ be a polarized irreducible holomorphic symplectic fourfold deformation equivalent to $S^{[2]}$, where $S$ is a K3 surface. Let $\mathrm{N}^1_+(F,g)$ be the positive hal…