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

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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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Commutative Algebra, Algebraic Geometry, 13A35; 13D02; 13D40; 14H60

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http://salesiana.dossiersoluciones.com/handle/123456789/70136

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0402180
 http://arxiv.org/abs/math/0402180

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arXiv