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Upper bounds of Hilbert coefficients and Hilbert functions

  • JUAN ELIAS (a1)
Abstract
Abstract

Let (R, m) be a d-dimensional Cohen–Macaulay local ring. In this paper we prove, in a very elementary way, an upper bound of the first normalized Hilbert coefficient of a m-primary ideal IR that improves all known upper bounds unless for a finite number of cases, see Remark 2.3. We also provide new upper bounds of the Hilbert functions of I extending the known bounds for the maximal ideal.

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[3] J. Elias . On the first normalized Hilbert coefficient. J. Pure Appl. Alg. 201 (2005), 116125.

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[6] M. E. Rossi . A bound on the reduction number of a primary ideal. Proc. Amer. Math. Soc. 128 (2000), 13251332.

[7] M. E. Rossi and G. Valla . The Hilbert function of the Ratliff–Rush filtration. J. Pure Appl. Alg. 201 (2005), 2541.

[8] M. E. Rossi , G. Valla and W. V. Vasconcelos . Maximal Hilbert functions. Result. Math. 39 (2001), 99114.

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[10] B. Singh . Effect of a permisible blowing-up on the local Hilbert function. Inv. Math. 26 (1974), 201212.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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