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arXiv · 0911.0278

Hurwitz equivalence of braid monodromies and extremal elliptic surfaces

Alex Degtyarev
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Abstract

We discuss the equivalence between the categories of certain ribbon graphs and subgroups of the modular group $Γ$ 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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Alex Degtyarev. 2009-11-02. Hurwitz equivalence of braid monodromies and extremal elliptic surfaces. https://doi.org/10.1112/plms%2Fpdr013

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