Geography of irreducible plane sextics

We complete the equisingular deformation classification of irreducible singular plane sextic curves. As a by-product, we also compute the fundamental groups of the complement of all but a few maximizing sextics

Oka's conjecture on irreducible plane sextics

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.Comment: Final version accepted for publicatio

Plane sextics with a type E7 singular point

Ankara : The Department of Mathematics and the Institute of Engineering and Science of Bilkent University, 2011.Thesis (Master's) -- Bilkent University, 2011.Includes bibliographical references leaves 30-31.The computation of the fundamental grup of a plane sextic (i.e., curves B ⊂ P 2 ) still remain unanswered problem. There is an huge effort on this subject. In this thesis, we study plane sextic curves with a type E7 singular point, try to state a geometric approach to compute the fundamental groups of plane sextics with that type of singular points and develop a trick to find the commutant of these groups.Aktaş, Mehmet EminM.S