Hilbert-Kunz multiplicity of powers of ideals in dimension two
Alessandro De Stefani, Shreedevi K. Masuti, Maria Evelina Rossi, Jugal, K. Verma
TL;DR
This paper investigates how the Hilbert-Kunz multiplicity of ideal powers behaves in two-dimensional local rings, addressing open problems and providing new criteria related to Ratliff-Rush multiplicities.
Contribution
It offers new insights and criteria for Hilbert-Kunz multiplicity of ideal powers in dimension two, solving some open problems posed by Smirnov.
Findings
Provides answers to open problems in dimension two
Introduces a Ratliff-Rush based criterion for Hilbert-Kunz multiplicity
Enhances understanding of the behavior of multiplicities in local rings
Abstract
We study the behavior of the Hilbert-Kunz multiplicity of powers of an ideal in a local ring. In dimension two, 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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Taxonomy
TopicsCommutative Algebra and Its Applications · Advanced Banach Space Theory · Rings, Modules, and Algebras