6 problems

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 $S$ be a smooth projective surface. A symplectic automorphism is an automorphism acting trivially on the space of holomorphic two-forms $H^{2,0}(S)$. It acts on the Albanese ke…

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…

Conway-group classification conjecture. There is a bijective correspondence between finite groups of symplectic automorphisms of manifolds of $K3^{[n]}$ type (for some $n$) and sub…

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…