Hurwitz equivalence of braid monodromies and extremal elliptic surfaces

Details Hurwitz equivalence of braid monodromies and extremal elliptic surfaces Hurwitz equivalence of braid monodromies and extremal elliptic surfaces

2009-11-02

arxiv.org/abs/0911.0278v1

Proc. London Math. Soc. (2011) 103 (6): 1083-1120

Mathematics

Algebraic Geometry

Scientific paper

10.1112/plms/pdr013

We discuss the equivalence between the categories of certain ribbon graphs and subgroups of the modular group $\Gamma$ and use it to construct exponentially large families of not Hurwitz equivalent simple braid monodromy factorizations of the same element. As an application, we also obtain exponentially large families of {\it topologically} distinct algebraic objects such as extremal elliptic surfaces, real trigonal curves, and real elliptic surfaces.

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