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 $2$.
Citation
Kei-Ichi Watanabe. Ken-Ichi Yoshida. "Hilbert-Kunz multiplicity of two-dimensional local rings." Nagoya Math. J. 162 87 - 110, 2001.
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