2 problems

Let $X$ be an irreducible holomorphic symplectic manifold deformation equivalent to O'Grady's $10$-dimensional exceptional example. Monodromy-isometry conjecture.…

Let $X$ be deformation equivalent to a generalized Kummer variety of dimension $2n$, with $n\geq 2$. Then $H^2(X,\mathbb Z)$ is isometric to…