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      Hurwitz equivalence of braid monodromies and extremal elliptic surfaces

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      Author
      Degtyarev, A.
      Date
      2011
      Source Title
      Proceedings of the London Mathematical Society
      Print ISSN
      0024-6115
      Electronic ISSN
      1460-244X
      Publisher
      Wiley
      Volume
      103
      Issue
      6
      Pages
      1083 - 1120
      Language
      English
      Type
      Article
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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 this equivalence 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 topologically distinct algebraic objects such as extremal elliptic surfaces, real trigonal curves, and real elliptic surfaces. © 2011 London Mathematical Society.
      Permalink
      http://hdl.handle.net/11693/21682
      Published Version (Please cite this version)
      http://dx.doi.org/10.1112/plms/pdr013
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