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

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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
##### Publication
Received: 9 November 2014
Revised: 22 March 2015
Accepted: 10 May 2015
Published: 29 February 2016
Proposed: Richard Thomas
Seconded: Walter Neumann, Jim Bryan
##### Authors
 Benoît Guerville-Ballé Tokyo Gakugei University Department of Mathematics Koganeishi Tokyo 184-8501 Japan http://www.benoit-guervilleballe.com