3 problems

K-semistable-domain conjecture. The set $\operatorname{Kss}(X,\sum_{j=1}^k D_j)$ is a polytope in $\overline{\Delta^k}$; all of its extremal points are rational; and all its extrem…

Let $X$ be a smooth projective variety, let $V$ be a fixed sheaf on $X$, and let $P$ be a moduli space of pairs consisting of a sheaf $F$ and a map $V\to F$, with universal pair…

Let $X/Z$ be a proper morphism, let $D$ be the divisor in the log adjunction setup, and let $\mathcal D{}^{\mathrm{mm}}$ denote its maximal moduli b-divisor. Let $\mathcal P$ be a…