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

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

2002-11-30

arxiv.org/abs/math/0212002v2

Math. Research Letters 10 (2003), 423-434

Mathematics

Commutative Algebra

12 pages. In a two-dimensional regular local ring with algebraically closed residue field, every complete fractionary ideal is

Scientific paper

There has arisen in recent years a substantial theory of "multiplier ideals'' in commutative rings. These are integrally closed ideals with properties that lend themselves to highly interesting applications. But 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 "complete.") However, among multiplier ideals arising from an integer multiplying constant (also known as adjoint ideals) the only simple complete ones primary for the maximal ideal are those of order one.

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