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Hilbert–Kunz Multiplicity and an Inequality between Multiplicity and Colength

✍ Scribed by Kei-ichi Watanabe; Ken-ichi Yoshida

Book ID
102574410
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
176 KB
Volume
230
Category
Article
ISSN
0021-8693

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✦ Synopsis

In this paper, we study local rings of small Hilbert-Kunz multiplicity. In particular, we prove that an unmixed local ring of Hilbert-Kunz multiplicity one is regular and classify two-dimensional Cohen-Macaulay local rings whose Hilbert-Kunz multiplicity is 2 or less. Also, we investigate the inequality between the multiplicity and the colength of the tight closure of parameter ideals inverse to the usual inequality between multiplicity and colength.

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✍ N. Fakhruddin; V. Trivedi 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 262 KB

We compute the Hilbert-Kunz functions and multiplicities for certain projective embeddings of ag varieties G=B and elliptic curves, over algebraically closed ÿelds of positive characteristics. The group theoretic nature of both these classes of examples is used, albeit in di erent ways, to explicitl