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2023-05-02

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cc-by-sa (c) Marchesi, S. et al., 2023
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/208003

Triangular arrangements on the projective plane

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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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Geometria discreta, Àlgebra homològica, Singularitats (Matemàtica)

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Discrete geometry, Homological algebra, Singularities (Mathematics)

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MARCHESI, Simone and VALLÈS, Jean. Triangular arrangements on the projective plane. Epijournal de Geometrie Algebrique. 2023. Vol. 7. ISSN 2491-6765. [consulted: 14 of August of 2026]. Available at: https://hdl.handle.net/2445/208003

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