Integrally Closed Finite-colength Ideals in Two-dimensional Regular Local Rings Are Multiplier Ideals
نویسنده
چکیده
Introduction. There has arisen in recent years a substantial body of work on “multiplier ideals” in commutative rings (see [La]). Multiplier ideals are integrally closed ideals with properties that lend themselves to highly interesting applications. One is tempted then to ask just how special multiplier ideals are among integrally closed ideals in general. In this note we show that in a two-dimensional regular local ring R with maximal ideal m such that the residue field R/m is algebraically closed there is in fact no difference between multiplier ideals and integrally closed ideals, at least when we deal with finite-colength ideals (i.e., those containing a power of m):
منابع مشابه
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 “complete.”...
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