The rationality of the Hilbert-Kunz multiplicity in graded dimension two

Abstract

We show that the Hilbert-Kunz multiplicity is a rational number for an R_+-primary homogeneous ideal I=(f_1, ..., f_n) in a two-dimensional graded domain R of finite type over an algebraically closed field of positive characteristic. Moreover we give a formula for the Hilbert-Kunz multiplicity in terms of certain rational numbers coming from the strong Harder-Narasimhan filtration of the syzygy bundle Syz(f_1, . . ., f_n) on the projective curve Y = Proj R.

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References in corpus (1)

• Tight closure and plus closure in dimension two

Cited by in corpus (3)

• Hilbert-Kunz Functions for Normal Rings
• Restriction of the cotangent bundle to elliptic curves and Hilbert-Kunz fnctions
• A Hilbert-Kunz criterion for solid closure in dimension two (characteristic zero)