Fundamental Groups of Some Special Quadric Arrangements

Abstract

Continuing our work on the fundamental groups of conic-line arrangements [3], we obtain presentations of fundamental groups of the complements of three families of quadric arrangements in P2. The first arrangement is a union of n conics, which are tangent to each other at two common points. The second arrangement is composed of n quadrics which are tangent to each other at one common point. The third arrangement is composed of n quadrics, n−1 of them are tangent to the nth one and each one of the n − 1 quadrics is transversal to the other n − 2 ones.