Simone Marchesi ; Jean Vallès - Triangular arrangements on the projective plane

epiga:7323 - Épijournal de Géométrie Algébrique, 2 mai 2023, Volume 7 - https://doi.org/10.46298/epiga.2023.7323
Triangular arrangements on the projective planeArticle

Auteurs : Simone Marchesi ; Jean Vallès

    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.


    Volume : Volume 7
    Publié le : 2 mai 2023
    Accepté le : 15 janvier 2023
    Soumis le : 1 avril 2021
    Mots-clés : Mathematics - Algebraic Geometry,Mathematics - Algebraic Topology,Mathematics - Combinatorics,52C35, 14F06, 32S22

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