Nagoya Mathematical Journal

Hilbert-Kunz multiplicity of two-dimensional local rings

Kei-Ichi Watanabe and Ken-Ichi Yoshida

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Abstract

We study the behavior of Hilbert-Kunz multiplicity for powers of an ideal, especially the case of stable ideals and ideals in local rings of dimension $2$. We can characterize regular local rings by certain equality between Hilbert-Kunz multiplicity and usual multiplicity.

We show that rings with "minimal" Hilbert-Kunz multiplicity relative to usual multiplicity are "Veronese subrings" in dimension $2$.

Article information

Source
Nagoya Math. J., Volume 162 (2001), 87-110.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631592

Mathematical Reviews number (MathSciNet)
MR1836134

Zentralblatt MATH identifier
1018.13008

Subjects
Primary: 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
Secondary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05] 13H15: Multiplicity theory and related topics [See also 14C17] 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]

Citation

Watanabe, Kei-Ichi; Yoshida, Ken-Ichi. Hilbert-Kunz multiplicity of two-dimensional local rings. Nagoya Math. J. 162 (2001), 87--110. https://projecteuclid.org/euclid.nmj/1114631592


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