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

epiga:7323 - Épijournal de Géométrie Algébrique, May 2, 2023, Volume 7
Triangular arrangements on the projective plane

Authors: 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
    Published on: May 2, 2023
    Submitted on: April 1, 2021
    Keywords: Mathematics - Algebraic Geometry,Mathematics - Algebraic Topology,Mathematics - Combinatorics,52C35, 14F06, 32S22

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