4 problems

Let $T$ be a hyperkähler variety. Write $\operatorname{CH}^1(T)$ for the divisor classes, $c_i(T)$ for the Chern classes of $T$, and $\mathrm{cl}$ for the cycle class map. Beauvill…

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…

Let $X$ be a projective hyper-Kähler manifold, and let $\operatorname{CH}^*(X)$ denote its Chow ring with $\mathbb{Q}$-coefficients. Beauville's conjecture. The cycle class map is…

Voisin's injectivity conjecture. The restriction