Geometry & Topology

An arithmetic Zariski $4$–tuple of twelve lines

Benoît Guerville-Ballé

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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.

Article information

Geom. Topol., Volume 20, Number 1 (2016), 537-553.

Received: 9 November 2014
Revised: 22 March 2015
Accepted: 10 May 2015
First available in Project Euclid: 16 November 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32S22: Relations with arrangements of hyperplanes [See also 52C35]
Secondary: 32Q55: Topological aspects of complex manifolds 54F65: Topological characterizations of particular spaces

line arrangements combinatorics topological type Zariski pair


Guerville-Ballé, Benoît. An arithmetic Zariski $4$–tuple of twelve lines. Geom. Topol. 20 (2016), no. 1, 537--553. doi:10.2140/gt.2016.20.537.

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