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arXiv · 1904.11222

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

Rodolfo Aguilar
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Abstract

Let $\mathscr{A}$ be a real projective line arrangement and $M(\mathscr{A})$ its complement in $\mathbb{CP}^2$. We obtain an explicit expression in terms of Randell's generators of the meridians around the exceptional divisors in the blow-up $\bar{X}$ of $\mathbb{CP}^2$ in the singular points of $\mathscr{A}$. We use this to investigate the partial compactifications of $M(\mathscr{A})$ contained in $\bar{X}$ 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.

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Rodolfo Aguilar. 2019-04-25. The fundamental group of partial compactifications of the complement of a real line arrangement. https://arxiv.org/abs/1904.11222

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