An Explicit Method to Write Belyi Morphisms

Details An Explicit Method to Write Belyi Morphisms An Explicit Method to Write Belyi Morphisms

2010-11-25

arxiv.org/abs/1011.5644v2

Mathematics

Algebraic Geometry

11 pages, 15 figures

Scientific paper

In this work, for an infinite family of embedded graphs on the sphere we explicitly calculate the corresponding Belyi morphisms. The importance of the family relies on the fact that the associated triangulation is non-negatively curved, and hence is canonically an element of the lattice W. Thurston has found in [Thu98]. This settles a non-trivial relationship in between. We, further, propose a method to deal with curves of higher genus.

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