Foldable fans, cscK surfaces and local K-moduli

Puntos clave

• All foldable surfaces classified in this study admit a constant scalar curvature Kähler metric, affirming their geometric relevance.
• The moduli space of polarised cscK surfaces locally resembles a finite quotient of a toric affine variety with terminal singularities.
• The introduction of foldable surfaces offers a novel perspective on the study of moduli spaces surrounding toric geometric structures.
• This research contributes to the understanding of the relationship between lattice automorphism groups and the existence of cscK metrics.