Integral Closures of Ideals in Completions of Regular Local Domains

In this paper we exhibit an example of a three-dimensional regular local domain (A,n) having a height-two prime ideal P with the property that the extension P of P to the n-adic completion  of A is not integrally closed. We use a construction we have studied in earlier papers: For R = k[x, y, z], where k is a field of characteristic zero and x, y, z are indeterminates over k, the example A is an intersection of the localization of the power series ring k[y, z][[x]] at the maximal ideal (x, y, z) with the field k(x, y, z, f, g), where f, g are elements of (x, y, z)k[y, z][[x]] that are algebraically independent over k(x, y, z). The elements f, g are chosen in such a way that using results from our earlier papers A is Noetherian and it is possible to describe A as a nested union of rings associated to A that are localized polynomial rings over k in five variables.