3 problems

Let $Y$ be a general Artin–Mumford quartic double solid, let $Y'$ be its blow-up at its $10$ singular points, and let $X$ be the Enriques surface associated to $Y$. Let…

Rationality conjecture for $\mathbb{Q}$-factorial nodal quartic double solids. Every $\mathbb{Q}$-factorial nodal quartic double solid is irrational.

Let $V$ and $W$ be four-dimensional vector spaces, let $s:W\subset S^2V^\vee$ be a generic embedding, and let $D\subset\mathbb{P}(W)\cong\mathbb{P}^3$ be the associated quartic sym…