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Journal of the London Mathematical Society Advance Access published online on June 6, 2008
Journal of the London Mathematical Society, doi:10.1112/jlms/jdn029
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© 2008 London Mathematical Society

Oka's conjecture on irreducible plane sextics

Alex Degtyarev

Department of Mathematics
Bilkent University
06800 Ankara
Turkey

We partially prove and partially disprove Oka's conjecture on the fundamental group/Alexander polynomial of an irreducible plane sextic. Among other results, we enumerate all irreducible sextics with simple singularities admitting dihedral coverings and find examples of Alexander equivalent Zariski pairs of irreducible sextics.

2000 Mathematics Subject Classification 14H30 (primary); 14J28 (secondary).

Received February 28, 2007; revised February 26, 2008;
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