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oai:recercat.cat:2445/2080032025-12-05T09:55:40Zcom_2072_1057col_2072_478917col_2072_478920

Triangular arrangements on the projective plane Marchesi, Simone Vallès, Jean Geometria discreta Àlgebra homològica Singularitats (Matemàtica) Discrete geometry Homological algebra Singularities (Mathematics) 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. 2024-02-23T10:24:39Z 2024-02-23T10:24:39Z 2023-05-02 2024-02-23T10:24:39Z info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 2491-6765 https://hdl.handle.net/2445/208003 741086 eng Reproducció del document publicat a: Epijournal de Geometrie Algebrique, 2023, vol. 7 cc-by-sa (c) Marchesi, S. et al., 2023 http://creativecommons.org/licenses/by-sa/4.0/ info:eu-repo/semantics/openAccess 20 p. application/pdf Episciences Articles publicats en revistes (Matemàtiques i Informàtica)