6 problems

Let $X$ be a hyper-Kähler variety. Write $A^\ast(X)$ for its Chow ring with rational coefficients, and let $c_j(T_X)$ denote the Chern classes of its tangent bundle. Beauville–Vois…

Let $T$ be a hyperkähler variety, and let $\operatorname{CH}^1(T)$ denote its divisor classes. The cycle class map sends algebraic cycles to rational cohomology. Beauville's diviso…

Let $Y$ be a double EPW quartic, and let the subgroup of $\operatorname{CH}^2(Y)$ generated by constant cycle surfaces be understood as the subgroup of codimension-two cycles repre…

Beauville--Voisin conjecture. The restriction of the cycle class map to $\langle c_i(X),\operatorname{Pic}(X)\rangle$ is injective. Equivalently, any polynomial in line bundles and…

Let $X$ be a hyper-Kähler variety of dimension $2n$. For each $i$, let $C_{2n-i}(X)\subset \operatorname{CH}^i(X)$ be the $\mathbb{Q}$-vector space generated by codimension-$i$ sub…

Voisin's injectivity conjecture. The restriction