Zariski pairs of conic-line arrangements of degrees 7 and 8 via fundamental groups

Abstract

We find a new Zariski pair with non-isomorphic fundamental groups that consists of degree $ 8 $ conic-line arrangements. Each arrangement has three conics and two lines. We use the Zariski-van Kampen Theorem and some known Coxeter groups to determine the fundamental groups. Two examples of degree $7$ Zariski pairs that were introduced in 2014 by the last named author, are given as well. They consist of a pair of conic-line arrangements with three conics in each (and thus, each has a single line) and a pair with two conics in each (and thus, each has three lines). We were able to provide alternative proof of the fact those are indeed Zariski pairs by our methods.