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

Let $M$ be a projective hyperkähler variety. A Lagrangian covering family for $M$ is a closed subscheme $\mathcal{U}\subset M\times B$, pure of dimension $\dim(B)+n$, where…

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…