Combinatorial symmetry of line arrangements and applications

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

doi:10.1016/j.topol.2015.07.004

Combinatorial symmetry of line arrangements and applications

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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 language	English
Pages (from-to)	226-247
Number of pages	22
Journal	Topology and its Applications
Volume	193
DOIs	https://doi.org/10.1016/j.topol.2015.07.004
State	Published - 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V.

Funding

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 .

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

Keywords

Falk-Sturmfels
Matroid
Oriented matroid
Pseudoline arrangement
Rybnikov

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10.1016/j.topol.2015.07.004

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AU - Cohen, Moshe

AU - Sun, Hao

AU - Teicher, Mina

AU - Ye, Fei

AU - Zarkh, Anna

PY - 2015

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KW - Falk-Sturmfels

KW - Matroid

KW - Oriented matroid

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ER -

Combinatorial symmetry of line arrangements and applications

Abstract

Bibliographical note

Funding

Keywords

Access to Document

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