Colarte Gómez, LienaCosta Farràs, LauraMarchesi, SimoneMiró-Roig, Rosa M. (Rosa Maria)Salat Moltó, Martí2023-03-082023-03-082021-12-190025-5874https://hdl.handle.net/2445/194820In 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 $\mathcal{A}$.25 p.application/pdfengcc by (c) Liena Colarte-Gómez et al., 2021http://creativecommons.org/licenses/by/3.0/es/Geometria algebraicaAnells commutatiusHomologiaAlgebraic geometryCommutative ringsHomologyinfo:eu-repo/semantics/article7174562023-03-08info:eu-repo/semantics/openAccess