3 problems

Let $X$ be a fourfold of $K3^{[2]}$-type admitting a symplectic involution $\sigma$, let $Y$ be the partial resolution of $X/\sigma$, and let $S$ be the K3 surface contained in…

Let $\pi: \mathscr{S} \to B$ be a family of surfaces over an analytic space $B$, and call a point of $B$ very general if it lies outside a countable union of proper analytic subset…

Let $S$ be a smooth projective surface over the complex numbers. Write $T_S$ for the integral polarized Hodge structure on the transcendental part of $H^2(S,\mathbb Z)$. Nondecompo…