Fundamental Group of Sextics of Torus Type

  • Mutsuo Oka
  • Duc Tai Pho
Part of the Trends in Mathematics book series (TM)


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 {C 3,9, 3A2} and the fundamental group is bigger than ℤ2 * ℤ3. In fact, the Alexander polynomial is given by (t 2t+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.


Modulus Space Fundamental Group Tangent Cone Surjective Homomorphism Alexander Polynomial 
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Copyright information

© Springer Basel AG 2002

Authors and Affiliations

  • Mutsuo Oka
    • 1
  • Duc Tai Pho
    • 1
  1. 1.Department of MathematicsTokyo Metropolitan UniversityTokyoJapan

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