4 problems

Let $f:X\to S$ be a smooth family from a Kähler manifold $X$ onto a smooth, connected, relatively compact curve $S$. Assume that $(X,B+\boldsymbol{\beta})$ is a generalized klt pai…

Fix a positive integer $n$ and a real number $\varepsilon>0$. Let $\mathfrak{D}$ be the set of all log pairs $(X,\Delta)$ such that $X$ is a projective variety of dimension $n$,…

Let $L$ be a line bundle equipped with two continuous metrics ${\|\ \|}_1$ and ${\|\ \|}_2$, and let $\operatorname{vol}(L, {\|\ \|}_1,{\|\ \|}_2)$ be the non-archimedean volume de…

Let $n\in\mathbb{N}$ and let $I\subset [0,1]$ satisfy the descending chain condition. Let $\mathfrak{D}$ be the set of simple normal crossings pairs $(X,\Delta)$ such that $X$ is a…