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=(f1, ..., fn) 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(f1, . . ., fn) on the projective curve Y = Proj R.
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