8 problems

Let $X$ be a smooth projective variety and let $L$ be an ample line bundle on $X$. A Lefschetz decomposition of $\mathit{D}^b(X)$ is minimal when it is strict and minimal with resp…

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…

Extended Dubrovin conjecture. If $\mathrm{BQH}(X)$ is generically semisimple and $[K_X]$ is invertible in $\mathrm{QH}(X)_{can}$, then there is an exceptional collection…

Let $\mathsf{A}$ be the K3 category of the Debarre–Voisin hyperplane section $Y$, and let $T$ and $P$ be the associated congruence of lines and Peskine variety. Let $\mathcal{U}$ a…

Let $W$ be a $7$-dimensional vector space, let $X\subset\operatorname{Gr}(3,W)$ be the $5$-dimensional zero locus of a section of…

Let $X=\operatorname{Gr}(k,n)$, let $\mathcal U$ be the tautological subbundle, and let $\mathcal A_i$ be the full triangulated subcategories defined in the source using the specif…

Let $X=\operatorname{Gr}(k,n)$, let $\mathcal U$ be the tautological subbundle, and let $\mathcal A_i$ be the full triangulated subcategories generated by the specified Schur power…

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…