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 C[subscript 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 ≥ −2, the Hilbert series of C[subscript A,k] is not determined by the matroid of A for k ≤ −6.National Science Foundation (U.S.) (CAREER Award DMS-0504629