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      Plane sextics with a type e8 singular point

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      Author
      Degtyarev, A.
      Date
      2010
      Source Title
      Tohoku Mathematical Journal
      Print ISSN
      0040-8735
      Electronic ISSN
      2186-585X
      Publisher
      Tohoku Daigaku Suugaku Kyoshitsu
      Volume
      62
      Pages
      329 - 355
      Language
      English
      Type
      Article
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      Abstract
      We construct explicit geometric models for and compute the fundamental groups of all plane sextics with simple singularities only and with at least one type E8 singular point. In particular, we discover four new sextics with nonabelian fundamental groups; two of them are irreducible. The groups of the two irreducible sextics found are finite. The principal tool used is the reduction to trigonal curves and Grothendieck’s dessins d’enfants.
      Keywords
      Plane sextic
      Singular curve
      Fundamental group
      Trigonal curve
      Dessin d’enfant
      Permalink
      http://hdl.handle.net/11693/48317
      Published Version (Please cite this version)
      https://doi.org/10.2748/tmj/1287148615
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      • Department of Mathematics 614
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