7 problems

Let $X^{2n}$ be an irreducible holomorphic symplectic manifold equipped with an abelian fibration whose fibres have polarization type $(1,\ldots,1,n+1)$. Assume the fibration admit…

Let $X$ be an abelian surface, let $K_n(X)$ be the generalized Kummer variety, and let $z=\{z_0,\ldots,z_n\}\in K_n(X)$ with $z_m\in X$. For a point $z$, let $O_z$ denote its ratio…

Let $(X,\alpha)$ be a twisted abelian surface, let $K=K_\sigma(X,\alpha,\mathbf{v})$ be the kernel of the Albanese map, and suppose that $\dim K=2n$. For $E\in K$, let $O_E$ denote…

Let $M$ be a holomorphic symplectic variety of generalized Kummer type and dimension $2n$, and let $R\in H_2(M,\mathbb{Z})$ be the class of a line in a Lagrangian $n$-plane in $M$.…

Let $X$ be an irreducible holomorphic symplectic manifold deformation equivalent to a $2n$-dimensional generalized Kummer variety. Let $Mon^2(X)$ denote its degree-two monodromy gr…

Let $X$ be deformation equivalent to a generalized Kummer variety of dimension $2n$, with $n\geq 2$. Then $H^2(X,\mathbb Z)$ is isometric to…

Let $(X,g)$ be a polarized variety deformation equivalent to a four-dimensional generalized Kummer variety. Let $(R,R)$ denote the Beauville–Bogomolov form on homology. The general…