28 problems

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

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…

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

Let $(X,B)$ be a pair, and let $f\colon X\to S$ be a contraction such that $-(K_X+B)$ is nef over $S$. For an arbitrary schematic point $s\in S$, let $f^{-1}(s)$ denote the scheme-…

Generalized canonical bundle formula conjecture. Theorem should remain valid even without assuming that $f$ is projective and that $B+\boldsymbol{\beta}_X$ is big.

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.

Base-point-freeness conjecture. The class $K_X + B + \alpha$ should be semiample: there should exist a holomorphic morphism $f:X\to Y$ onto a compact Kähler space and a Kähler clas…

Let $(X,B,\mathbf{M})$ be a projective log canonical generalized pair over the complex numbers, with generalized log canonical divisor $K_X+B+\mathbf{M}_X$. A divisor is numericall…

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 $s$ be a natural number and let $\epsilon$ be a positive real number. Assume $(Z,\Delta+\mathbf N)$ is an $\epsilon$-lc generalized pair of dimension $s$ with a closed point…

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 $d$ and $p$ be positive integers, and let $\mathcal{I}\subseteq[0,1]\cap\mathbb{Q}$ be a DCC set. Consider a projective rationally connected lc generalized pair…

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 $d\in\mathbb{Z}_{>0}$ 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…

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

Let $d$ be a positive integer, let $\epsilon$ be a positive real number, and let $\Gamma\subseteq[0,1]$ be a DCC set. A generalized pair $(X,B+M)$ has data…

Strong $(\delta,n)$-complement conjecture. There exist a natural number $n$ and a non-negative real number $\delta$, depending only on $d,p,\epsilon$ and $\Lambda$, such that for e…

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…

Weak non-vanishing and weak abundance for g-pairs. 1. There exists an effective $R$-divisor $N$ such that

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