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

Research paper by Le Van Dinh

Indexed on: 07 Apr '14Published on: 07 Apr '14Published in: Mathematics - Combinatorics



Abstract

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.