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

Abstract

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.

The fundamental group of quotients of products of some topological spaces by a finite group - A generalization of a Theorem of Bauer-Catanese-Grunewald-Pignatelli: Le groupe fondamental de quotients de produits de certains espaces topologiques par ungroupe fini — Généralisation d’un théorème de Bauer–Catanese–Grunewald–Pignatelli

“…The original motivation of this work was to study the partial compactifications of the complement of an arrangement of lines in P 2 C which is the topic of my Ph.D. thesis. In [Agu19] a general method for computing a presentation of the fundamental group was given and some examples studied. A family of arrangements related to the studied in op.…”