Hilbert-Kunz multiplicity of two-dimensional local rings

Authors
Watanabe, KI Yoshida, KI
Citation
Ki. Watanabe et Ki. Yoshida, Hilbert-Kunz multiplicity of two-dimensional local rings, NAG MATH J, 162, 2001, pp. 87-110
Citations number
32
Categorie Soggetti
Mathematics
Journal title
NAGOYA MATHEMATICAL JOURNAL
ISSN journal
00277630 → ACNP
Volume
162
Year of publication
2001
Pages
87 - 110
Database
ISI
SICI code
0027-7630(200106)162:<87:HMOTLR>2.0.ZU;2-X
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 dimensio n 2. We can characterize regular local rings by certain equality between Hi lbert-Kunz multiplicity and usual multiplicity. We show that rings with "minimal" Hilbert-Kunz multiplicity relative to usu al multiplicity are "Veronoese subrings" in dimension 2.