2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70136We 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.Some minor changesCommutative AlgebraAlgebraic Geometry13A35; 13D02; 13D40; 14H60text