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. More specific, 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=ProjR.
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