A Conjecture on Poincaré-Betti Series of Modules of Differential Operators on a Generic Hyperplane Arrangement

Abstract

Holm [Holm 04, Holm 02] studied modules of higher-order differential operators (generalizing derivations) on generic (central) hyperplane arrangements. We use his results to determine the Hilbert series of these modules. We also give a conjecture about the Poincaré-Betti series; these are known for the module of derivations through the work of Yuzvinsky [Yuzvinsky 91] and Rose and Terao [Rose and Terao 91]

Keywords:

• Primary 13N10, 14J70
• Ring of differential operators
• hyperplane arrangement
• free resolution