6 problems

Let $X$ be a Calabi–Yau variety in one of the cases under consideration, and let $\operatorname{Aut}(X)$ act on its Kähler cone. A Kawamata–Morrison conjecture. The action of…

Wilson's conjecture. The Kähler cone of $X$ should be rational and finitely generated in $N^1(X)$.

Let the Kähler cone be the set of Kähler classes, and let the extremal Kähler cone be the subset consisting of classes represented by extremal Kähler metrics. Suppose the flow equa…

Let $X$ be a Calabi–Yau manifold with a chosen complex structure and suppose that $h^{2,0}(X)=0$. Let … let $\mathcal{K}$ be the Kähler cone of $X$, and let $\mathcal{K}_+$ be the…

Let $X$ be a compact Kähler manifold and let $C\subset X$ be a smooth curve with ample normal bundle. Write $[C]$ for its cohomology class and let $\mathcal{K}(X)$ denote the Kähle…

Wilson's weaker cone conjecture. If $c_2$ is strictly positive on the closure of the Kähler cone of a Calabi–Yau threefold, then the Kähler cone of $Z$ is generated by finitely man…