An arithmetic Zariski 4–tuple of twelve lines

Guerville-Ballé, Benoît

doi:10.2140/gt.2016.20.537

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An arithmetic Zariski $4$–tuple of twelve lines

Benoît Guerville-Ballé

Geometry & Topology 20 (2016) 537–553

DOI: 10.2140/gt.2016.20.537

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

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

Volume 20, issue 1 (2016)