Plane sextics via dessins d'enfants

Abstract

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.

a few points clarified; final version accepted for publication

References in corpus (7)

• Oka's conjecture on irreducible plane sextics
• Oka's conjecture on irreducible plane sextics. II
• On deformation types of real elliptic surfaces
• Stable symmetries of plane sextics
• A plane sextic with finite fundamental group
• Fundamental groups of symmetric sextics. II
• Alexander-equivalent Zariski pairs of irreducible sextics

Cited by in corpus (3)

• Plane sextics with a type ${\mathbf{E}}_8$ singular point
• Plane sextics with a type ${\mathbf{E}}_6$ singular point
• The fundamental group of a generalized trigonal curve