Classification of Morrison–Kawamata dream surfaces

Classify Morrison–Kawamata dream surfaces in dimension two, including the broader class of surfaces satisfying the axiomatized Morrison–Kawamata cone conjecture.

Background

The paper observes that its finiteness argument for Calabi–Yau surfaces extends to varieties satisfying the Morrison–Kawamata cone conjecture, provided that every klt pair admits a good minimal model. It further notes that Morrison–Kawamata dream spaces provide a broader framework, and identifies the classification of surfaces in this class as unresolved.