3 problems

Let $P$ be a Fano polygon, that is, a two-dimensional Fano polytope. Call $P$ symmetric when its symmetry group is nontrivial. Hacking–Kim conjecture. If $P$ is a Kähler–Einstein F…

Let $P$ be a smooth Fano polytope, and let $B(P)$ denote its barycentric transformation. A Fano polytope is of type $B_\infty$ when the barycentric transformation can be applied in…

Conjecture A. There exists a bijective correspondence between the set of mutation-equivalence classes of Fano polygons and the set of qG-deformation equivalence classes of locally…