The fundamental group of a generalized trigonal curve

Abstract

We develop a modification of the Zariski--van Kampen approach for the computation of the fundamental group of a trigonal curve with improper fibers. As an application, we list the deformation families and compute the fundamental groups of all irreducible maximizing simple sextics with a type $\mathbf{D}$ singular point.

References in corpus (5)

• Plane sextics via dessins d'enfants
• Stable symmetries of plane sextics
• Plane sextics with a type ${\mathbf{E}}_8$ singular point
• Transcendental lattice of an extremal elliptic surface
• Plane sextics with a type ${\mathbf{E}}_6$ singular point