6 problems

Let $X_1$ and $X_2$ be Gushel–Mukai varieties, and let $\mathsf{A}(X1)$ and $\mathsf{A}(X2)$ be their associated Lagrangian subspaces. Assume that neither subspace contains decompo…

Generic projected-push-forward conjecture. For every $[E]\in U$, the object $\operatorname{pr}_X(j_*E)$ is $\sigma_X$-semistable.

Let $X$ and $X'$ be GM varieties of the same dimension. The Kuznetsov–Perry conjecture. If there exists an equivalence … then $X$ and $X'$ are birationally equivalent. This conject…

Let $X_1$ and $X_2$ be Gushel–Mukai varieties of the same dimension, and let $\mathcal{K}\!u(X_i)$ denote their Kuznetsov components. Birational categorical Torelli conjecture. If…

Let $X$ be a GM fourfold. An associated K3 surface of $X$ is a K3 surface arising from a period point of $X$ lying on a hypersurface $\mathcal{D}_d$, with a nef algebraic class $h$…

Let $X$ be a rational Gushel–Mukai fourfold, and let $\mathcal{A}_X$ denote its GM category. A rationality conjecture. Then … for some K3 surface $S$. This is the GM analogue of th…