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J. Korean Math. Soc. 2003; 40(2): 169-177

Printed March 1, 2003

Copyright © The Korean Mathematical Society.

The Hilbert-Kunz multiplicity of two-dimensional toric rings

Sangki Choi and Seokyoung Hong

Konkuk University

Abstract

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Recently, K. Watanabe showed that the Hilbert-Kunz multiplicity of a toric ring is a rational number. In this paper we give an explicit formula to compute the Hilbert-Kunz multiplicity of two-dimensional toric rings. This formula also shows that the Hilbert-Kunz multiplicity of a two-dimensional non-regular toric ring is at least $3/2$.

Keywords: Hilbert-Kunz multiplicity, normal semi-group, toric ring

MSC numbers: 13H15, 14B05, 14H20

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