Correction to “Combinatorics and geometry of power ideals”: Two counterexamples for power ideals of hyperplane arrangements
We disprove Holtz and Ron’s conjecture that the power ideal CA,−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 ≥ −2, the Hilbert series of CA,k is not determined by the matroid of A for k ≤ −6. Remark. This note is a corrigendum to our article [1], and we follow the notation of that paper.