Triangulations of the sphere and degenerations of K3 surfaces

Details Triangulations of the sphere and degenerations of K3 surfaces Triangulations of the sphere and degenerations of K3 surfaces

2008-09-05

arxiv.org/abs/0809.0937v1

Mathematics

Algebraic Geometry

37 pages

Scientific paper

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.

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