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Hilbert-Kunz multiplicity of three-dimensional local rings | Kei-ichi Watanabe
; Ken-ichi Yoshida
; | Date: |
22 Jul 2003 | Subject: | Commutative Algebra MSC-class: Primary 13D40 Secondary 13A35, 13H05, 13H10, 13H15 | math.AC | Affiliation: | Nihon University), Ken-ichi Yoshida (Nagoya University | Abstract: | In this paper, we investigate a lower bound (say $s_{HK}(p,d)$) on Hilbert-Kunz multiplicities for non-regular unmixed local rings of Krull dimension $d$ with characteristic $p>0$. Especially, we focus three-dimensional local rings. In fact, as a main result, we will prove that $s_{HK}(p,3) = 4/3$ and that a three-dimensional complete local ring of Hilbert-Kunz multiplicity 4/3 is isomorphic to the non-degnerate quadric hyperplanes $k[[X,Y,Z,W]]/(X^2+Y^2+Z^2+W^2)$ under mild conditions. Furthermore, we pose a generalization of the main theorem to the case of $dim A ge 4$ as a conjecture, and show that it is also true in case of $dim A = 4$ using the similar method as in the proof of the main theorem. | Source: | arXiv, math.AC/0307294 | Services: | Forum | Review | PDF | Favorites |
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