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 $\mathbb{CP}^2$.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2014
- DOI:
- 10.48550/arXiv.1411.2300
- arXiv:
- arXiv:1411.2300
- Bibcode:
- 2014arXiv1411.2300G
- Keywords:
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- Mathematics - Geometric Topology;
- 32S22;
- 32Q55;
- 54F65
- E-Print:
- 14 pages, 8 figures