Triangular arrangements on the projective plane

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 arrang...

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Detalles Bibliográficos
Autores: Marchesi, Simone, Vallès, Jean
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/208003
Acceso en línea:https://hdl.handle.net/2445/208003
Access Level:acceso abierto
Palabra clave:Geometria discreta
Àlgebra homològica
Singularitats (Matemàtica)
Discrete geometry
Homological algebra
Singularities (Mathematics)
Descripción
Sumario: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.