Hypertetrahedral arrangements

In this paper, we introduce the notion of a complete hypertetrahedral arrangement $\mathcal{A}$ in $\mathbb{P}^n$. We address two basic problems. First, we describe the local freeness of $\mathcal{A}$ in terms of smaller complete hypertetrahedral arrangements and graph theory properties, specializin...

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Detalles Bibliográficos
Autores: Colarte Gómez, Liena, Costa Farràs, Laura, Marchesi, Simone, Miró-Roig, Rosa M. (Rosa Maria), Salat Moltó, Martí
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/194820
Acceso en línea:https://hdl.handle.net/2445/194820
Access Level:acceso abierto
Palabra clave:Geometria algebraica
Anells commutatius
Homologia
Algebraic geometry
Commutative rings
Homology
Descripción
Sumario:In this paper, we introduce the notion of a complete hypertetrahedral arrangement $\mathcal{A}$ in $\mathbb{P}^n$. We address two basic problems. First, we describe the local freeness of $\mathcal{A}$ in terms of smaller complete hypertetrahedral arrangements and graph theory properties, specializing the Mustață-Schenck criterion. As an application, we obtain that general complete hypertetrahedral arrangements are not locally free. In the second part of this paper, we bound the initial degree of the first syzygy module of the Jacobian ideal of $\mathcal{A}$.