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 ${\mathbb{CP}}^2$.

14 pages, 8 figures

References in corpus (1)

• A topological invariant of line arrangements

Cited by in corpus (5)

• An arithmetic Zariski pair of line arrangements with non-isomorphic fundamental group
• Fundamental groups of real arrangements and torsion in the lower central series quotients
• Orbits in $({\mathbb{P}}^r{)}^n$ and equivariant quantum cohomology
• On the non-connectivity of moduli spaces of arrangements: the splitting-polygon structure
• Configurations of points and topology of real line arrangements