Plane sextics with a type E7 singular point

Abstract

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.