English

Fundamental group of sextics of torus type

Algebraic Geometry 2007-05-23 v1

Abstract

We show that the fundamental group of the complement of any irreducible tame torus sextics in P2\bf P^2 is isomorphic to Z2Z3\bf Z_2*\bf Z_3 except one class. The exceptional class has the configuration of the singularities {C3,9,3A2}\{C_{3,9},3A_2\} and the fundamental group is bigger than Z2Z3\bf Z_2*\bf Z_3. In fact, the Alexander polynomial is given by (t2t+1)2(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.

Keywords

Cite

@article{arxiv.math/0010182,
  title  = {Fundamental group of sextics of torus type},
  author = {Mutsuo Oka and Duc Tai Pho},
  journal= {arXiv preprint arXiv:math/0010182},
  year   = {2007}
}

Comments

27 pages, 14 figures