1997/11/12 by Eriko Hironaka, Hironaka, Eriko · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9711016
Latex, 22 pages, 15 figures
arxiv created 1997/11/12 · openalex publication_date 1997/11/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we describe the complement of real line arrangements in the complex plane in terms of the boundary three-manifold of the line arrangement. We show that the boundary manifold of any line arrangement is a graph manifold with Seifert fibered vertex manifolds, and depends only on the incidence graph of the arrangement. When the line arrangement is defined over the real numbers, we show that the homotopy type of the complement is determined by the incidence graph together with orderings on the edges emanating from each vertex.