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 (4)

• Oka's conjecture on irreducible plane sextics
• Oka's conjecture on irreducible plane sextics. II
• A plane sextic with finite fundamental group
• Pencils and Infinite Dihedral covers of P^2

Cited by in corpus (16)

• Oka's conjecture on irreducible plane sextics
• Oka's conjecture on irreducible plane sextics. II
• Geography of irreducible plane sextics
• Plane sextics via dessins d'enfants
• Stable symmetries of plane sextics
• A plane sextic with finite fundamental group
• Mordell-Weil lattices and toric decompositions of plane curves
• On the Artal--Carmona--Cogolludo construction
• On plane sextics with double singular points
• Lattice Zariski k-ples of plane sextic curves and Z-splitting curves for double plane sextics
• Alexander-equivalent Zariski pairs of irreducible sextics
• Dihedral coverings of trigonal curves
• Plane sextics with a type ${\mathbf{E}}_6$ singular point
• Zariski $k$-plets via dessins d'enfants
• Apparent contours of nonsingular real cubic surfaces
• Irreducible plane sextics with large fundamental groups