7 problems

Let $Y$ be a singular variety admitting crepant categorical resolutions, and call a categorical resolution indecomposable when it has no nontrivial decomposition in the relevant ca…

Let $Y$ be a singular variety, and let a categorical resolution of $Y$ correspond to a Lefschetz decomposition of $4D^b(\mathit{Z})4D$, where $\mathit{Z}$ is the exceptional diviso…

Let $C$ be the singular Coble cubic, let $W$ be the associated smooth variety, let $q^*W$ be its indicated $\mathbb{P}^1$-bundle, and let $\Gamma$ be the associated genus-$2$ curve…

Let $W$ be a vector space of dimension $m$, and let $\operatorname{Pf}(2k,W)$ denote the closure of the locus of bivectors in $\Lambda^2W$ of rank $2k$. Let…

Let $Y$ be a quasiprojective scheme. A categorical resolution of $Y$ is a smooth triangulated category $\mathcal{T}$ equipped with adjoint functors…

Drinfeld's conjecture. The DG enhancement of $D^b_{\operatorname{coh}}(\mathcal D_X)$ has a smooth categorical compactification.

Let $X$ be a smooth projective variety. A minimal Lefschetz decomposition of $\D^b(X)$ is a Lefschetz decomposition whose first block is minimal under inclusion, and a categorical…