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arxiv: 1411.2300 · v2 · pith:5HQL75SJnew · submitted 2014-11-09 · 🧮 math.GT

An arithmetic Zariski 4-tuple of twelve lines

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keywords arrangementsarithmeticcombinatorialdifferentfourinformationsamezariski
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Using the invariant developed in [6], 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 couples of arrangements among this 4-tuplet form new arithmetic Zariski pairs, i.e. a couple of arrangements with the same combinatorial information but with different embedding in $\mathbb{CP}^2$.

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