8 problems

Let $X$ be a holomorphic symplectic $4$-fold and let $M_\beta$ be the moduli scheme of one-dimensional stable sheaves $F$ on $X$ with $\operatorname{ch}_3(F)=\beta$ and $\chi(F)=1$…

Let $X$ be a holomorphic symplectic $4$-fold, let $\beta\beta\in H_2(X,\mathbb{Z})$ be a primitive curve class, and let $n_{0,\beta}(\gamma_1,\ldots,\gamma_n)$,…

Let $X$ be a variety of $K3^{[n]}$ type and let $\beta\in H_2(X,\mathbb{Z})$ be effective. For each divisor $k\mid\beta$, choose a variety $X_k$ of $K3^{[n]}$ type and a parallel t…

Let $X$ be a projective irreducible holomorphic symplectic variety of dimension $2n$. A primitive rational curve means a rational curve whose cohomology class is primitive. Voisin'…

Let $X$ be a smooth projective holomorphic symplectic variety. A marking of $X$ is required to satisfy Condition $(\star)$, namely that the small diagonal is distinguished with res…

Let $X$ be a smooth projective holomorphic symplectic variety. Write $\operatorname{CH}(X)$ for its Chow ring with rational coefficients and $\overline{\operatorname{CH}}(X)$ for t…

Let $X$ be a holomorphic symplectic variety, let $\operatorname{CH}(X)_{(0)}$ denote the degree-zero part of the Chow grading associated with a Chow--Künneth decomposition, and let…

Let $X$ be a holomorphic symplectic variety of dimension $2n$. Then the motivic splitting property. there is a canonical self-dual multiplicative Chow–Künneth decomposition … of Bl…