An arithmetic Zariski 4-tuple of twelve lines

Abstract

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 $\mathbb{CP}^2$.