8 problems

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…

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…

A rational Calabi–Yau pair is a three-dimensional pair $(X,D)$ that is rational, has index one, and has coregularity $0$. Toric-model conjecture. Every three-dimensional rational C…

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…

Let $(X,D)$ be a klt Calabi–Yau pair of dimension $n$, with standard coefficients, so that $K_X+D\sim_{\mathbb Q}0$. Its minimal log discrepancy is denoted by…

Let $(X,\Delta)$ be a klt Calabi–Yau pair. Let … where $N^1(X)_{\mathbb{Q}}$ is the rational Néron–Severi space of $X$, and let $\operatorname{Nef}^e(X)$ denote the nef effective c…

Kawamata–Morrison–Totaro Cone Conjecture. There exists a rational polyhedral cone $\Pi$ in $\operatorname{Nef}^e(X)$ that is a fundamental domain for the action of…

Let $Q$ be a connected component of the coarse moduli space of triples $(X,E=E_1+\dots+E_n,\Theta)$, where $X$ is a connected smooth projective complex variety,…