English

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

Commutative Algebra 2007-05-23 v3 Algebraic Geometry

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. 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.

Keywords

Cite

@article{arxiv.math/0402180,
  title  = {The rationality of the Hilbert-Kunz multiplicity in graded dimension two},
  author = {Holger Brenner},
  journal= {arXiv preprint arXiv:math/0402180},
  year   = {2007}
}

Comments

Some minor changes