Correction to “Combinatorics and geometry of power ideals”: Two counterexamples for power ideals of hyperplane arrangements

Source abstract

We disprove Holtz and Ron’s conjecture that the power ideal C A , − 2 C_{\mathcal {A},-2} of a hyperplane arrangement A \mathcal {A} (also called the internal zonotopal space) is generated by A \mathcal {A} -monomials. We also show that, in contrast with the case k ≥ − 2 k \geq -2 , the Hilbert series of C A , k C_{\mathcal {A},k} is not determined by the matroid of A \mathcal {A} for k ≤ − 6 k \leq -6 .