Plane sextics with a type singular point
arXiv:0902.2281
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 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 {\it dessins d'enfants}