We study the behavior of the Hilbert-Kunz multiplicity of powers of an ideal in a local ring. In dimension 2, we provide answers to some problems raised by Smirnov, and give a criterion to answer one of his questions in terms of a "Ratliff-Rush version" of the Hilbert-Kunz multiplicity.
Hilbert–Kunz multiplicity of powers of ideals in dimension two
De Stefani A.;Rossi M. E.;
2025-01-01
Abstract
We study the behavior of the Hilbert-Kunz multiplicity of powers of an ideal in a local ring. In dimension 2, we provide answers to some problems raised by Smirnov, and give a criterion to answer one of his questions in terms of a "Ratliff-Rush version" of the Hilbert-Kunz multiplicity.
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