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Plane sextics via dessins d’enfants. (English) Zbl 1175.14024

Summary: We develop a geometric approach to the study of plane sextics with a triple singular point. As an application, we give an explicit geometric description of all irreducible maximal sextics with a type \(\mathbf E_7\) singular point and compute their fundamental groups. All groups found are finite; one of them is nonabelian.

MSC:

14H57 Dessins d’enfants theory
14H45 Special algebraic curves and curves of low genus
14H30 Coverings of curves, fundamental group
14H50 Plane and space curves

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