Two counterexamples for power ideals of arrangements
arXiv:1211.1368
Abstract
We disprove Holtz and Ron's conjecture that the power ideal C_{A,-2} of a hyperplane arrangement A (also called the "internal zonotopal space") is generated by A-monomials. We also show that, in contrast with the case k \geq -2, the Hilbert series of C_{A,k} is not determined by the matroid of A for k \leq -6.
This short note is a corrigendum to our paper "Combinatorics and geometry of power ideals"