6 problems

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

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…