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arXiv · 2008.00384

Multiplicity sequence and integral dependence

Claudia Polini·Ngo Viet Trung·Bernd Ulrich·Javid Validashti
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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.

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Claudia Polini, Ngo Viet Trung, Bernd Ulrich, Javid Validashti. 2020-08-02. Multiplicity sequence and integral dependence. https://doi.org/10.1007/s00208-020-02059-5

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