English

Hypertetrahedral arrangements

Algebraic Geometry 2021-11-02 v1

Abstract

In this paper, we introduce the notion of a complete hypertetrahedral arrangement A\mathcal{A} in Pn\mathbb{P}^{n}. We address two basic problems. First, we describe the local freeness of A\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 A\mathcal{A}.

Keywords

Cite

@article{arxiv.2111.01116,
  title  = {Hypertetrahedral arrangements},
  author = {Liena Colarte and Laura Costa and Simone Marchesi and Rosa Maria Miró-Roig and Marti Salat},
  journal= {arXiv preprint arXiv:2111.01116},
  year   = {2021}
}

Comments

26 pages. To appear in Mathematische Zeitschrift. Comments are welcome

R2 v1 2026-06-24T07:21:25.996Z