The fundamental group of partial compactifications of the complement of a real line arrangement

摘要

Let A be a real projective line arrangement and M(A) its complement in CP2. We obtain an explicit expression in terms of Randell's generators of the meridians around the exceptional divisors in the blow-up (X) over bar of CP2 in the singular points of A. We use this to investigate the partial compactifications of M(A) contained in (X) over bar 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. (C) 2020 Elsevier B.V. All rights reserved.