Conjugation-free geometric presentations of fundamental groups of arrangements

The fundamental group of the complement of a line and conic-line arrangement in the plane plays an important
role in studying these arrangements. We introduce the notion of a conjugation-free geometric presentation
for such fundamental groups. The main motivation for defining this presentation is due to the fact that for arrangements having such a
presentation, its lattice determines the fundamental group. We construct some families of line arrangements that have a conjugation-free geometric presentation and some families of conic-line arrangement that exhibit special phenomena.