3 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 $g$ tend to infinity, let $\boldsymbol{\boldsymbol{k}}=(k_1,\ldots,k_n)$ be a partition of $2g-2$, and write ${\rm Vol}(k_1,\ldots,k_n)$ for the volume of the corresponding str…