#### Volume 20, issue 1 (2016)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear Contacts ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
An arithmetic Zariski $4$–tuple of twelve lines

### Benoît Guerville-Ballé

Geometry & Topology 20 (2016) 537–553
##### Abstract

Using the invariant developed by E Artal, V Florens and the author, we differentiate four arrangements with the same combinatorial information but in different deformation classes. From these arrangements, we construct four other arrangements such that there is no orientation-preserving homeomorphism between them. Furthermore, some pairs of arrangements among this 4–tuple form new arithmetic Zariski pairs, ie a pair of arrangements conjugate in a number field with the same combinatorial information but with different embedding topology in $ℂ{ℙ}^{2}$.

##### Keywords
line arrangements, combinatorics, topological type, Zariski pair
##### Mathematical Subject Classification 2010
Primary: 32S22
Secondary: 32Q55, 54F65