8 problems

Log termination conjecture. Every sequence of $K_X+B$-flips terminates.

Strong $b5$-lc complement conjecture. For every $0<b5$ and $d$, there exists a finite set $a9_{b5,d}$ of positive integers such that every such pair has an $(b5,n)$-complement over…

Weak $b5$-lc complement conjecture. For every $0<b4$ and $d$, there exist a finite set $a9_{b4,d,91b}$ of positive integers and $0<b5$ such that every such pair is $(b5,n)$-complem…

Let $(X,\Delta)$ be a Kawamata log terminal (klt) pair. The numerical abundance conjecture asserts that the numerical and Iitaka dimensions of the log canonical divisor coincide: ……

Minimal model conjecture. If $K_{X}+\Delta$ is pseudo-effective, then $(X,\Delta)$ has a good minimal model; if $K_{X}+\Delta$ is not pseudo-effective, then $(X,\Delta)$ has a Mori…

Generalized Iitaka conjecture. One has

Generalized log minimal model conjecture. The pair $(X/Z,B)$ has either a Mori fibre space or a log minimal model $(Y/Z,B_Y)$; if $K_Y+B_Y$ is nef$/Z$, then it is semi-ample$/Z$; a…

Length-bound conjecture. The estimate $\leq 2\dim X$ should be replaced by $\leq \dim X+1$; that is, one should be able to choose $C$ with