5 problems

Let $(X,\Delta)$ be a projective log canonical pair of dimension $n$. Log canonical model conjecture. If $K_X+\Delta$ is big, then $(X,\Delta)$ has a log canonical model. The sourc…

Chow quotient and log canonical model conjecture. The inclusion $X(r,n)\subset \overline{X}(r,n)$ is the log canonical model precisely in the cases

Existence conjecture for log canonical models. The graded ring of $\cal O_S$-modules

Fix $d\in\mathbb N$, $v\in\mathbb R_{>0}$, and a DCC set $I\subset(0,1]$. For a projective klt pair $(X,D)$ with $\dim X=d$ and $D\in I$, let $\operatorname{Ivol}(K_X+D)$ be its Ii…

Broustet–Höring's conjecture. The morphism $\mu$ is an isomorphism in codimension one.