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arXiv · 1903.08885

Triangular arrangements on the projective plane

Simone Marchesi·Jean Vallès
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Abstract

In this work we study line arrangements consisting in lines passing through three non-aligned points. We call them triangular arrangements. We prove that any combinatorics of a triangular arrangement is always realized by a Roots-of-Unity-Arrangement, which is a particular class of triangular arrangements. Among these Roots-of Unity-Arrangements, we provide conditions that ensure their freeness. Finally, we give two triangular arrangements having the same weak combinatorics, such that one is free but the other one is not.

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Simone Marchesi, Jean Vallès. 2019-03-21. Triangular arrangements on the projective plane. https://doi.org/10.46298/epiga.2023.7323

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