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.

arXiv comment37 pages

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