  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.
