English

An arithmetic Zariski 4-tuple of twelve lines

Geometric Topology 2016-03-09 v2

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 CP2\mathbb{CP}^2.

Keywords

Cite

@article{arxiv.1411.2300,
  title  = {An arithmetic Zariski 4-tuple of twelve lines},
  author = {Benoît Guerville-Ballé},
  journal= {arXiv preprint arXiv:1411.2300},
  year   = {2016}
}

Comments

14 pages, 8 figures

R2 v1 2026-06-22T06:52:55.942Z