The nodal classes conjecture for holomorphic symplectic fourfolds

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 extremal elements of $E^*$ in the closure of the cone $\mathrm{N}_E(F,g)$. For $R\in E^*_{\mathrm{nod}}$, let $\lambda$ be any nef and big divisor class satisfying $R.\lambda=0$. Nodal classes conjecture. Each nodal class $R\in E^*_{\mathrm{nod}}$ represents a rational curve contracted by a birational morphism given by sections of $\mathcal O_F(m\lambda)$ for $m\gg0$. If $(R,R)=-\frac12$ or $-2$, the corresponding $(-2)$-class $\rho$ is represented by a family of rational curves parametrized by a K3 surface, which are blown down to rational double points. If $(R,R)=-\frac52$, the corresponding $(-10)$-class $\rho$ is represented by a family of lines contained in a $\mathbb P^2$ contracted to a point. The conjecture specifies the geometric behavior of the nodal classes and their associated contractions; its status is not resolved in the supplied source context.