The Core of a Module over a Two-Dimensional Regular Local Ring

Abstract

This paper explicitly determines the core of a torsion-free, integrally closed module over a two-dimensional regular local ring. It is analogous to a result of Huneke and Swanson which determines the core of an integrally closed ideal. The main result asserts that the core of a finitely generated, torsion-free, integrally closed module over a two-dimensional regular local ring is the product of the module and a certain Fitting ideal of the module. The technical tools used are quadratic transforms and Buchsbaum–Rim multiplicity.