7 problems

Let $X$ be a $K3$ surface. The group ${\operatorname{Aut}}_s(X)$ of symplectic automorphisms, namely automorphisms acting trivially on a nonzero holomorphic $2$-form, acts on Bloch…

Let $X$ be a $K3$ surface, and let ${\operatorname{Aut}}_s(X)$ be the group of symplectic automorphisms of $X$, meaning automorphisms that act trivially on a nonzero holomorphic…

Let $n>2$ and let $X$ be a manifold of type $\mathrm{K3}^{[n]}$. A finite group of symplectic automorphisms of $X$ is a finite group acting on $X$ while preserving its holomorphic…

For a manifold of $K3^{[n]}$ type, let $S_G$ be the coinvariant lattice associated with a symplectic automorphism group $G$, and let $A_{S_G}$ be its discriminant group. Mongardi's…

Let $L_G$ be a lattice of type (a) or (b), let $L^G$ be the associated invariant lattice, let $A_{L^G}$ be its discriminant group, and let $\overline{O}(L^G)$ denote the image of i…

Uniqueness conjecture. For a fixed abstract group type of $H$ (equivalently, a fixed $n$) and a fixed Dynkin-diagram type of degeneration, the corresponding lattice

Let $X$ be a hyperkähler manifold deformation equivalent to the Hilbert square of a $K3$ surface, and let $\varphi$ be an involution of $X$ preserving the holomorphic symplectic fo…