Multiplicity sequence and integral dependence

Abstract

We prove that two arbitrary ideals $I\subset J$ in an equidimensional and universally catenary Noetherian local ring have the same integral closure if and only if they have the same multiplicity sequence. We also obtain a Principle of Specialization of Integral Dependence, which gives a condition for integral dependence in terms of the constancy of the multiplicity sequence in families.

17 pages, to be published in Math. Ann

References in corpus (1)

• Integral closure of ideals

Cited by in corpus (1)

• Computing multiplicity sequences