Tight closure, localization and Hilbert-Kunz theory

The tight closure operation of Hochster and Huneke attaches to each ideal I in a Noetherian integral domain containing Z/p an ideal I* containing I. Whether this operation always "commutes with localization" was long open and perplexing. Last year, Holger Brenner showed that some old calculations of mine, slightly augmented, would lead to a negative answer. (The calculations determined the Hilbert-Kunz functions of certain degree 4 plane curves in a 1-parameter family). I'll sketch the calculations, and derive a proof for the counterexample that's rather easy. Nothing about tight closure, other than it's definition, will be used.