11 problems

Existence of flips. The flip of $f$ exists.

Log termination conjecture. Every sequence of $K_X+B$-flips terminates.

Let $X$ be a normal projective variety, let $B\subset X$ be a $\mathbb{Q}$-Weil divisor such that $K_X+B$ is log terminal, and let $R\subset\overline{NE}(X)$ be an extremal ray wit…

Let $X_{\alpha}$ and $X_{\beta}$ be the varieties associated with the simple flip in Proposition, and let $D(X_{\alpha})$ and $D(X_{\beta})$ denote their triangulated derived categ…

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

Flip F-bound conjecture. If $F(Y)\leq 24$, then

Work in the setting of Cohen–Macaulay rational singularities. Let $N=H^0(\mathcal{V}_X)$, where $\mathcal{V}_X$ is the object from the paper’s contraction and tilting setup, and le…

Flip conjecture II. The sequence terminates after finitely many steps; equivalently, there is no infinite sequence of flips. The source explains that the minimal model program can…

Let $(X/Z,B)$ be a log canonical (lc) pair. A $(K_X+B)$-flip over $Z$ is a flip occurring in the log minimal model program, replacing a small contraction on which $K_X+B$ is negati…

Let $(X,H,\omega)$ be as in the analytic minimal model program, let $T_0<\infty$, and suppose that the semi-ample divisor $H+T_0K_X$ induces a contraction $\pi:X\to Y$ with…

Let $(X_0,B_0)\dashrightarrow (X_1,B_1)\dashrightarrow (X_2,B_2)\dashrightarrow\cdots$ be a sequence of log flips. Log flip termination conjecture. The sequence terminates after fi…