5 problems

Finite-generation conjecture. The ring $R(X,\Delta)$ is a finitely generated $\mathbb C$-algebra.

Finite generation conjecture for log canonical rings. The log canonical ring

Finite generation conjecture. The log canonical ring $R(X,\Delta)$ is finitely generated.

Let $f\colon X\to S$ be a proper surjective morphism between normal varieties, and let $B$ be a $\mathbb Q$-divisor on $X$ such that $(X,B)$ is log canonical. Relative finite gener…

Let $X$ be an $n$-dimensional smooth projective variety and let $B$ be a boundary $\mathbb Q$-divisor whose support is a simple normal crossing divisor on $X$. Assume that $K_X+B$…