4 problems

Let $\overline{\operatorname{M}}_{g,n}$ be the moduli space of stable $n$-pointed curves, and let $\overline{\operatorname{NE}}_1(\overline{\operatorname{M}}_{g,n})$ be its cone of…

Free-curve generation conjecture. Free rational curves generate the nef cone of curves.

Let $X_n$ be the blow-up of the projective plane at $n$ general points. Let $\mathcal{Q}_n$ be the nonnegative cone, let $\mathcal{Q}_n^{\succcurlyeq}$ denote its part in the indic…

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…