Let A be a real projective line arrangement and M (A) its complement in CP 2. We obtain an explicit expression in terms of Randell's generators of the meridians around the exceptional divisors in the blow-up ¯ X of CP 2 in the singular points of A. We use this to investigate the partial compactifications of M (A) contained in ¯ X and give a counterexample to a statement suggested by A. Dimca and P. Eyssidieux to the effect that the fundamental group of such an algebraic variety is finite whenever its abelianization is.