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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Bibliographic Details
Authors: Colarte Gómez, Liena, Costa Farràs, Laura, Marchesi, Simone, Miró-Roig, Rosa M. (Rosa Maria), Salat Moltó, Martí
Format: article
Status:Published version
Publication Date:2021
Country:España
Institution:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repository:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/194820
Online Access:https://hdl.handle.net/2445/194820
Access Level:Open access
Keyword:Geometria algebraica
Anells commutatius
Homologia
Algebraic geometry
Commutative rings
Homology
Description
Summary: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 $\mathcal{A}$.