6 problems

Minimal-model conjecture. Then $(X,B+M)$ has a minimal model.

Let $(X_1,B_1+M_1)$ be a projective $\mathbb{Q}$-factorial NQC dlt generalised pair such that $K_{X_1}+B_1+M_1$ is pseudoeffective. Consider a sequence of flips in a…

Let $(X_1,B_1+M_1)$ be a projective $\mathbb{Q}$-factorial NQC dlt generalised pair such that $K_{X_1}+B_1+M_1$ is pseudoeffective. Consider a $(K_{X_1}+B_1+M_1)$-MMP: … Let $S$ be…

Generalised abundance conjecture. If $K_X+B$ is pseudo-effective and $M$ is nef, then numerical abundance holds; equivalently, there is a semi-ample divisor $D$ such that

Generalised Shokurov conjecture under bounded fibre volume. There is a positive real number $\delta$, depending only on $d,v,\epsilon$, such that the coefficients of the discrimina…

Let $d$ be a natural number and let $\epsilon$ be a positive real number. Consider a generalised pair with data $X'\to X\overset{f}\to Z$ and $M'$, where $f$ is a contraction. The…