4 problems

Let $X$ be an irreducible holomorphic symplectic manifold of dimension $2g$, and let $q_X$ denote its Beauville–Bogomolov form. A line bundle $L$ on $X$ is called non-trivial if it…

Let $X$ be an irreducible symplectic manifold deformation equivalent to $(K3)^{[n]}$, let $(\,\ )$ be its Beauville form, and let $h\in H^{1,1}_{\mathbb Z}(X)$ satisfy $(h,h)=2$. F…

Let $n\geq 2$, and let $(X,H)$ be a degree-$2$ polarized irreducible symplectic variety, meaning that $X$ is an irreducible symplectic manifold deformation equivalent to…

Let $\pi\colon M\to B$ be the Lagrangian fibration under consideration, and let … be the associated complexes of coherent $\mathscr{O}_B$-modules, where $i$ records the cohomologic…