8 problems

Adjunction and effective adjunction conjectures. One can choose an effective representative $M_Z\geq 0$ in its $\mathbb{R}$-linear equivalence class such that $(Z,D_Z+M_Z)$ is log…

Let $f\colon X\to Z$ be the fibre space and let $D$, $\Theta$, $D_{\operatorname{div}}$, and $D_{\operatorname{mod}}$ be as in the paper's adjunction construction. Assume that $D$…

Let $f\colon X\to Z$ be a fiber space and let $D$ be a $\mathbb{Q}$-divisor on $X$ such that $(X,D)$ is log canonical and $K_X+D$ is $\mathbb{Q}$-linearly trivial over $Z$. Let…

Inversion of adjunction. Log canonicity of the induced foliated pair on the normalisation of $S$ should imply log canonicity of the original foliated pair near $S$.

Effective b-semiampleness conjecture. There exists a positive integer $I=I(d,\Gamma)$ such that, for every such $0$-contraction with $\dim X=d$ and $D^{\mathrm h}\in\Gamma$,…

Let $P\in X$ be the germ of a normal variety, and let $S+B$ be an effective $\mathbf{R}$-divisor on $X$ such that $S$ is a normal prime divisor not appearing in $B$. Assume that…

Let $X$ be a projective manifold of dimension $n$, and let $L$ be a strictly nef divisor, meaning that $L\cdot C>0$ for every irreducible curve $C$ on $X$. Adjoint strict-nefness c…

Let $R$ be an $F$-finite normal local ring of characteristic $p>0$, let $X:=\operatorname{Spec} R$, and let $D+B$ be an effective $\mathbb{Q}$-divisor on $X$, where $D$ is a normal…