Oka's conjecture on irreducible plane sextics

Abstract

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.

Final version accepted for publication

References in corpus (1)

• Oka's conjecture on irreducible plane sextics

Cited by in corpus (3)

• Oka's conjecture on irreducible plane sextics
• Stable symmetries of plane sextics
• Lattice Zariski k-ples of plane sextic curves and Z-splitting curves for double plane sextics