Combinatorial symmetry of line arrangements and applications

Meirav Amram, Moshe Cohen, Hao Sun, Mina Teicher, Fei Ye, Anna Zarkh

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


It is clear that a geometric symmetry of a line arrangement induces a combinatorial one; we study the converse situation. We introduce a strategy that exploits a combinatorial symmetry in order to produce a geometric reflection. We apply this method to disqualify three real examples found in previous work by the authors from being Zariski pairs. Robustness is shown by its application to complex cases, as well, including the MacLane and Nazir-Yoshinaga arrangements.

Original languageEnglish
Pages (from-to)226-247
Number of pages22
JournalTopology and its Applications
StatePublished - 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V.


This work was partially supported by the Emmy Noether Research Institute for Mathematics of the Minerva Foundation of Germany, the Oswald Veblen Fund , the Institute for Advanced Study , and the Polytechnic Institute of New York University .

FundersFunder number
Oswald Veblen Fund
Polytechnic Institute of New York University
Institute for Advanced Study


    • Falk-Sturmfels
    • Matroid
    • Oriented matroid
    • Pseudoline arrangement
    • Rybnikov


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