Integrally closed ideals in two-dimensional regular local rings are multiplier ideals

Multiplier ideals in commutative rings are certain integrally closed ideals with properties that lend themselves to highly interesting applications. How special are they among integrally closed ideals in general? We show that in a two-dimensional regular local ring with algebraically closed residue field there is in fact no difference between “multiplier” and “integrally closed” (or \hbox{“complete."}) But among multiplier ideals arising from an {\it integer\/} multiplying constant (also known as {\it adjoint\/} ideals), and primary for the maximal ideal, the only simple complete ideals are those of order one.}

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Published 1 January 2003