4 problems

Let $\pi:\mathcal X\to\Delta$ be a degeneration of an irreducible symplectic $2n$-fold. For each $m$, let $T_m$ be the associated monodromy operator on…

Let $\pi:\mathcal X\to\Delta$ be a degeneration of an irreducible symplectic $2n$-fold. For each $m$, let $T_m$ be the associated monodromy operator on…

Birationality and non-separatedness conjecture. The manifolds $X$ and $X'$ are birational if and only if they correspond to non-separated points in the moduli space.

Huybrechts–Sawon conjecture. If $L$ is isotropic with respect to the Beauville–Bogomolov quadratic form on $H^{2}(X,\mathbb{C})$ and $c_{1}(L)$ belongs to the birational Kähler con…