Topology and combinatorics of real line arrangements

By Enrique Artal Bartolo, J. Ruber, J. Agustín, Miguel Ángel Marcos Buzunáriz. Compositio Mathematica, 2003

57 citations recorded by the source corpus.

We prove the existence of complexified real arrangements with the same combinatorics but different embeddings in ${\mathbb P}^2$. Such a pair of arrangements has an additional property: they admit conjugated equations on the ring of polynomials over ${\mathbb Q}(\sqrt{5})$.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/55943d66f4bb02ca9118a07b45ab78ef614cf99c

Citations in the corpus

• Generalized Lantern Relations and Planar Line Arrangements (2011, unknown): “): Let d p= d p(0) and d j i = d j i (g p(0)). Then looking at Figure 4, we see that the points L j 1 (g p(t));:::;L j k (g p(t)) rotate as a group 360in the counterclockwise direction as tranges in [0;1]. The corresponding mapping class on the bounded portion of F g p(0) enclosed by d p is the comp”