On rings with small Hilbert-Kunz multiplicity

dc.creatorBlickle, Manuel
dc.creatorEnescu, Florian
dc.date2003-08-04
dc.date.accessioned2026-07-07T07:41:49Z
dc.date.available2026-07-07T07:41:49Z
dc.descriptionA result of Watanabe and Yoshida says that an unmixed local ring of positive characteristic is regular if and only if its Hilbert-Kunz multiplicity is one. We show that, for fixed $p$ (characteristic) and $d$ (dimension), there exist a number $ε(d,p) > 0$ such that any nonregular unmixed ring $R$ has Hilbert-Kunz multiplicity at least $1+ε(d,p)$. We also show that local rings with sufficiently small Hilbert-Kunz multiplicity are Cohen-Macaulay and $F$-rational.
dc.description5 pages. to appear in Proc. AMS
dc.identifierhttps://arxiv.org/abs/math/0308022
dc.identifierhttp://arxiv.org/abs/math/0308022
dc.identifierProc. Amer. Math. Soc. 132 (2004), no. 9, 2505--2509
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122253
dc.subjectCommutative Algebra
dc.subjectAlgebraic Geometry
dc.subject13A35
dc.titleOn rings with small Hilbert-Kunz multiplicity
dc.typetext

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