On the Gorensteinness of broken circuit complexes and Orlik–Terao ideals

It is proved that the broken circuit complex of an ordered matroid is Gorenstein if and only if it is a complete intersection. Several characterizations for a matroid that admits such an order are then given, with particular interest in the h-vector of broken circuit complexes of the matroid. As an application, we prove that the Orlik–Terao algebra of a hyperplane arrangement is Gorenstein if and only if it is a complete intersection. Interestingly, our result shows that the complete intersection property (and hence the Gorensteinness as well) of the Orlik–Terao algebra can be determined from the last two nonzero entries of its h-vector.