Lengths and multiplicities of integrally closed modules over a two-dimensional regular local ring

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.”...

Integrally Closed Finite-colength Ideals in Two-dimensional Regular Local Rings Are Multiplier Ideals

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-dim...

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

Integrally Closed Modules and their Divisors

There is a beautiful theory of integral closure of ideals in regular local rings of dimension two, due to Zariski, several aspects of which were later extended to modules. Our goal is to study integral closures of modules over normal domains by attaching divisors/determinantal ideals to them. They will be of two kinds: the ordinary Fitting ideal and its divisor, and another ‘determinantal’ idea...

rigid resolution of a finitely generated module over a regular local ring