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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 2.

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