Triangulations of the sphere and degenerations of K3 surfaces

Abstract

W. Thurston proved that to a triangulation of the sphere of non-negative combinatorial curvature, one can associate an element in a certain lattice over the Eisenstein integers such that its orbit is a complete invariant of the triangulation. In this paper, we show that this association can be obtained naturally by using Type III degenerations of K3 surfaces.

37 pages

Cited by in corpus (2)

• Compactifications of moduli of elliptic K3 surfaces: stable pair and toroidal
• On the GHKS compactification of the moduli space of K3 surfaces of degree two