6 problems

Let $S$ be a polarized K3 surface in $\mathfrak{M}_{\operatorname{BE}}(2t)$ with $t\geq 2$. For some $a$ satisfying $a^2\equiv -1\pmod{t}$, let…

Let $\wp\colon\operatorname{\mathbf{{M}}{}^{\mathrm{EPW}}}\to \mathcal{D}$ be the period map for double EPW sextics, and let $\mathcal{D}_2$, $\mathcal{D}_4$, and $\mathcal{D}_8$ b…

Let $\underline{\Lambda}$ be a Fano $10$-tuple of planes in $\mathbb{P}^5$, and let the objects associated with it be as in Proposition cited in the source, including the EPW sexti…

For a projective quotient variety $X$, let $E^\ast(X^r)\subset A^\ast(X^r)$ be the $\mathbb{Q}$-subalgebra generated by pullbacks of elements of $A^1(X)$ and $A^2(X)$, pullbacks of…

Let $\mathcal C$ be the class of varieties whose Chow rings admit the multiplicative bigrading described in Beauville's weak splitting problem. Let $X$ be an EPW sextic, meaning a…

Double EPW-sextic conjecture. The birational alternative never occurs.