Fundamental group of sextics of torus type

Details Fundamental group of sextics of torus type Fundamental group of sextics of torus type

2000-10-18

arxiv.org/abs/math/0010182v1

Mathematics

Algebraic Geometry

27 pages, 14 figures

Scientific paper

We show that the fundamental group of the complement of any irreducible tame torus sextics in $\bf P^2$ is isomorphic to $\bf Z_2*\bf Z_3$ except one class. The exceptional class has the configuration of the singularities $\{C_{3,9},3A_2\}$ and the fundamental group is bigger than $\bf Z_2*\bf Z_3$. In fact, the Alexander polynomial is given by $(t^2-t+1)^2$. For the proof, we first reduce the assertion to maximal curves and then we compute the fundamental groups for maximal tame torus curves.

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