3 problems

Let $(X,\lambda)$ be a polarized irreducible holomorphic symplectic manifold of $\mathrm{K3}^{[n]}$-type with $q_X(\lambda)=2$ and $\operatorname{div}(\lambda)=1$. Let…

Let $(X,\lambda)$ be a polarized irreducible holomorphic symplectic manifold of $\mathrm{K3}^{[n]}$-type with $q_X(\lambda)=2$, and let $\tau_{\lambda}$ be the associated antisympl…

O'Grady's conjecture. There exists an antisymplectic involution on $S^{[2]}$.