21 problems

Termination of flips. Any sequence of $K_X+B+\boldsymbol{\beta}_X$ flips is finite.

Existence of log terminal models. The pair $(X,B+\boldsymbol{\beta})$ has a log terminal model.

Minimal model conjecture. Then $(X/Z,B,\mathbf{M})$ has a minimal model.

Shokurov's boundedness of complements conjecture. There exists a constant $n$ depending only on $d$, $p$, and $R$ such that $K_{X'}+B'+M'$ has an $n$-complement…

Finite-coefficient conjecture. There exists a finite set $\Gamma_0\subset\Gamma$, depending only on $d$ and $\Gamma$, such that $B\in\Gamma_0$ and…

ACC conjecture for log canonical thresholds. The set

Generalized Kähler canonical bundle formula conjecture. If $f:(X,B+\boldsymbol\beta)\to Z$ is a generalized klt (respectively, lc) pair as above, then $(Z,B_Z+\boldsymbol\beta^Z)$…

Let $(X,\Delta)$ be a klt pair on a normal projective variety $X$ such that $K_X+\Delta$ is pseudo-effective. Let $L$ be a nef $\mathbb{Q}$-divisor on $X$. Generalized Nonvanishing…

Shokurov's conjecture. Fix a positive integer $r$ and a real number $0<\epsilon\leq 1$. There exists $\delta>0$ depending only on $r,\epsilon$ such that, if $\dim X-\dim Z=r$,…

Let $(X,\mathcal{F},B,\mathbf{M})$ be a generalized foliated quadruple. Here ACSS denotes the technical condition defined in the source, and F-dlt denotes foliated divisorial log t…

Let $(X,B,\mathbf{M})/U$ be an lc g-pair. The terms log resolution, descent of the b-divisor, and lc center are understood in the usual sense. The dlt characterization conjecture.…

Generalized complexity conjecture. The following statements hold:

Let $d$ be a positive integer and $\epsilon$ a positive real number. Let $(X,B+\mathbf{M})$ be a generalized pair of dimension $d$ and let $\pi:X\to Z$ be a contraction between pro…

Let $(X,\Delta+M)/Z$ be a generalized pair. Define … where $|X|_{\mathrm{cl}}$ denotes the set of all closed points of $X$ with the Zariski topology. Lower semi-continuity conjectu…

Let $d\in\mathbb{Z}_{>0}$ and let $I\subset[0,+\infty)$ be a subset satisfying the DCC. Define … where $M\in I$ has the meaning specified in the source's definition of generalized…

Numerical nonvanishing conjecture. There exists an effective $\mathbb{R}$-Cartier $\mathbb{R}$-divisor $D$ such that

Generalized diminished-base-locus conjecture. The diminished base locus

Let $(X',B'+M')$ be a generalized sub-pair with data $X\to X'$ and $M$, where $B'$, $M'$ and $M$ are $\mathbb{Q}$-divisors. Let $f\colon X'\to Z'$ be a contraction such that … Assu…

Existence of flips for g-lc pairs. The flip of every such flipping contraction exists.

Cone theorem for g-lc pairs. There are countably many curves $C_j\subset X$ such that $0<-(K_X+B+M)\cdot C_j\leq 2\dim X$ and

Birational weak Zariski decomposition conjecture. Every such pair admits a birational NQC weak Zariski decomposition over $Z$.