Topology and combinatorics of real line arrangements

Abstract

We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in the complex projective plane. Such pair of arrangements has an additional property: they admit conjugated equations on the ring of polynomials over the number field $\mathbb{Q}(\sqrt{5})$.

13 pages, 2 figures, accepted in Compositio Math

Cited by in corpus (6)

• An arithmetic Zariski 4-tuple of twelve lines
• Classification of Moduli Spaces of Arrangements of 9 Projective Lines
• An arithmetic Zariski pair of line arrangements with non-isomorphic fundamental group
• Fundamental groups of real arrangements and torsion in the lower central series quotients
• On complex line arrangements and their boundary manifolds
• Homology, lower central series, and hyperplane arrangements