4 problems

Kawamata–Morrison–Totaro cone conjecture. The group $\operatorname{Aut}(X/S,\Delta)$ acts on $\mathcal{A}^e(X/S)$ with finitely many orbits of Mori faces, while…

Let $(X,\Delta)$ be a klt Calabi–Yau pair. Let $\mathcal{B}^e(X)$ denote the effective cone appearing in the source, and let $PsAut(X,\Delta)$ act on it by pullback. Effective cone…

For every $n\geq 2$, let $m_n$ be the integer defined by the construction in Theorem. Let $(X,(1-b)S)$ be a complex klt Calabi–Yau pair of dimension $n$, where $S$ is a nonzero eff…

Gross–Hacking–Keel mirror construction conjecture. The free $R$-module $V$ with basis $U^{\mathrm{trop}}(\mathbb Z)$ has a natural finitely generated $R$-algebra structure whose st…