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arXiv · 2111.01116

Hypertetrahedral arrangements

Liena Colarte·Laura Costa·Simone Marchesi·Rosa Maria Miró-Roig·Marti Salat
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Abstract

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 Musta\c{t}\u{a}-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 $\mathcal{A}$.

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Liena Colarte, Laura Costa, Simone Marchesi, Rosa Maria Miró-Roig, Marti Salat. 2021-11-01. Hypertetrahedral arrangements. https://arxiv.org/abs/2111.01116

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