Nagoya Mathematical Journal

Bounds on the Hilbert-Kunz multiplicity

Olgur Celikbas, Hailong Dao, Craig Huneke, and Yi Zhang

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In this paper we give new lower bounds on the Hilbert-Kunz multiplicity of unmixed nonregular local rings, bounding them uniformly away from 1. Our results improve previous work of Aberbach and Enescu.

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Nagoya Math. J., Volume 205 (2012), 149-165.

First available in Project Euclid: 1 March 2012

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Primary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22]
Secondary: 13B22: Integral closure of rings and ideals [See also 13A35]; integrally closed rings, related rings (Japanese, etc.) 13H15: Multiplicity theory and related topics [See also 14C17] 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx]


Celikbas, Olgur; Dao, Hailong; Huneke, Craig; Zhang, Yi. Bounds on the Hilbert-Kunz multiplicity. Nagoya Math. J. 205 (2012), 149--165. doi:10.1215/00277630-1543805.

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