Geodesic
Triangular arrangements on the projective plane
Épijournal de Géométrie Algébrique, Tome 7 (2023)

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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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     author = {Marchesi, Simone and Vall\`es, Jean},
     title = {Triangular arrangements on the projective plane},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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     volume = {7},
     year = {2023},
     doi = {10.46298/epiga.2023.7323},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2023.7323/}
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Marchesi, Simone; Vallès, Jean. Triangular arrangements on the projective plane. Épijournal de Géométrie Algébrique, Tome 7 (2023). doi: 10.46298/epiga.2023.7323

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