6 problems

A 13-dimensional complex ball quotient is obtained from the Allcock lattice construction, with $X$ denoting the corresponding ball quotient and $X^{\rm sg}$ its singular or special…

Let the Deligne–Mostow theory produce ball quotients, and let moduli spaces of K3 surfaces denote the corresponding K3 moduli spaces. Dolgachev–Kondō's conjecture. All ball quotien…

Let the ordered moduli space of twelve points be the moduli space considered in the Deligne–Mostow setting for twelve points, and let a ball quotient model mean a realization by a…

Let $M$ be a compact complex manifold of complex dimension two equipped with a Kähler–Einstein metric and having negative sectional curvature. Si–Yau's conjecture. The manifold $M$…

Hurwitz ball quotient automorphism conjecture. Theorems concerning the bound $|\operatorname{Aut}(S)| \leq 288 e(S)$ and its equality case should hold without the arithmetic assump…

Deligne–Mostow arithmetic complex ball quotients are complex ball quotients arising from the moduli of K3 surfaces. Deligne–Mostow moduli conjecture. All Deligne–Mostow arithmetic…