Lower bounds for Hilbert-Kunz multiplicities in local rings of fixed dimension

2007/08/03 by Aberbach, Ian M., Enescu, Florian · 3 citations
#13A35 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.0708.0537

Abstract

Let (R,\m) be a formally unmixed local ring of positive prime characteristic and dimension d. We examine the implications of having small Hilbert-Kunz multiplicity (i.e., close to 1). In particular, we show that if R is not regular, there exists a lower bound, strictly greater than one, depending only on d, for its Hilbert-Kunz multiplicity.

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• Hilbert-Kunz multiplicity of quadrics decreases
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