Fundamental group of sextics of torus type

Original · EN

We show that the fundamental group of the complement of any irreducible tame torus sextics in P² is isomorphic to Z₂* Z₃ except one class. The exceptional class has the configuration of the singularities {C₃,₉,3A₂} and the fundamental group is bigger than Z₂* Z₃. In fact, the Alexander polynomial is given by (t²-t+1)². For the proof, we first reduce the assertion to maximal curves and then we compute the fundamental groups for maximal tame torus curves.