Hilbert-Kunz multiplicity of three-dimensional local rings
| dc.creator | Watanabe, Kei-ichi | |
| dc.creator | Yoshida, Ken-ichi | |
| dc.date | 2003-07-22 | |
| dc.date.accessioned | 2026-07-07T04:59:50Z | |
| dc.date.available | 2026-07-07T04:59:50Z | |
| dc.description | 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. | |
| dc.description | about 21 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0307294 | |
| dc.identifier | http://arxiv.org/abs/math/0307294 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68144 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Primary 13D40 Secondary 13A35, 13H05, 13H10, 13H15 | |
| dc.title | Hilbert-Kunz multiplicity of three-dimensional local rings | |
| dc.type | text |