5 problems

Kähler–Einstein polygon conjecture. All Kähler–Einstein Fano polygons are either triangles or symmetric.

Let $P$ be a Fano polygon. Two Fano polygons are mutation-equivalent if they lie in the same equivalence class under polygon mutations. A del Pezzo surface with cyclic quotient sin…

Mutation–deformation correspondence conjecture. There exists a bijective correspondence between the set of mutation-equivalence classes of Fano polygons and the set of $\mathbb{Q}$…

Period-determines-mutation conjecture. If $P_1$ and $P_2$ have the same singularity content and there is an affine-linear isomorphism $\varphi\colon L_{P_1}^T\to L_{P_2}^T$ such th…

Degree and ramification conjecture. The following hold: