A conjecture on Poincare-Betti series of modules of differential operators on a generic hyperplane arrangement

摘要

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 Poincare-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]