2 problems

Let $Y$ be the surface, let $D\subset Y$ be the boundary divisor, let $U=Y\setminus D$, and let $Z$ be the union of all $(-2)$ curves in $Y$. Write $Z'=Z\cap U$, let $\bar{Q}$ be t…

Let $\mathcal{C}$ be a $2$-Calabi-Yau triangulated category with cluster structure, let $T$ be a cluster tilting object, and let $\phi$ be a cluster map sending cluster tilting obj…