Hypertetrahedral arrangements

Abstract In this paper, we introduce the notion of a complete hypertetrahedral arrangement $${\mathcal {A}}$$ A in $${\mathbb {P}}^{n}$$ P n . We address two basic problems. First, describe local freeness terms smaller arrangements and graph theory properties, specializing Mustaţă–Schenck criterion. As an application, obtain that general are not locally free. second part bound initial degree first syzygy module Jacobian ideal