5 problems

O'Grady's conjecture. There is a positive integer $a\geq 1$ and a family of Lagrangian subvarieties $\pi:\mathcal{Z}_S\to X_n$ over a base $S$ such that $\mathcal{Z}_S$ covers…

Song's conjecture. The cohomology class of $P$ is

Song's conjecture. For an arbitrary hyperkähler variety, the norm of the line class satisfies

Let $X$ be a hyperkähler variety of dimension $2m$, and let $A^i(X):=CH^i(X)_{\mathbb{Q}}$ denote its codimension-$i$ Chow group with rational coefficients. Assume the Chow ring ha…

Let $Y$ be a bielliptic surface, let $f\colon X\to Y$ be its canonical covering of degree $n=2$, and let $w$ be a sheaf class on $Y$. Write $K_{X;f^*H,f^*A}(f^*w)$ and…