6 problems

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

Differentiability and orthogonality conjectures. The following two assertions are conjectured:

Let $X$ be the blow-up of ${\mathbb P}^2$ at a set of $n$ general points, let $H$ be the hyperplane class, and let $\mathbb E=E_1+\cdots+E_n$ be the exceptional divisor. Nagata's c…

Let $\overline{M}_{0,7}^{S_7}$ be the symmetric moduli space appearing in the source, and let $S_1,S_2,S_3,D_1,D_2$ be the classes used there. Define … A Zariski decomposition of…

Let $X$ be a smooth variety and let $\alpha\in\operatorname{BPF}_k(X)$, where $\operatorname{BPF}_k(X)$ denotes the cone of basepoint-free $k$-cycle classes. Let $\pi:Y\to X$ be a…

Let $X$ be a projective variety, let $\alpha$ be a cycle class admitting a Zariski decomposition, and write … Here $P(\alpha)$ and $N(\alpha)$ are respectively the positive and neg…