Hostname: page-component-5447f9dfdb-5flt4 Total loading time: 0 Render date: 2025-07-28T10:54:52.787Z Has data issue: false hasContentIssue false
  • English
  • Français

Upper bounds of Hilbert coefficients and Hilbert functions

Published online by Cambridge University Press:  01 July 2008

JUAN ELIAS
JUAN ELIAS*
Affiliation:
Departament d'Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain. e-mail: elias@ub.edu
Get access Rights & Permissions [Opens in a new window]

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 I ⊂ R 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.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 1 , July 2008 , pp. 87 - 94
Copyright
Copyright © Cambridge Philosophical Society 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Elias, J.. Characterization of the Hilbert-Samuel polynomials of curve singularities. Compositio Math. 74 (1990), 135–155.Google Scholar
[2]Elias, J.. On the deep structure of the blowing-up of curve singularities. Math. Proc. Camb. Phil. Soc. 131 (2001), 227–240.CrossRefGoogle Scholar
[3]Elias, J.. On the first normalized Hilbert coefficient. J. Pure Appl. Alg. 201 (2005), 116–125.CrossRefGoogle Scholar
[4]Lipman, J.. Stable ideals and Arf rings. Amer. J. Math. 93 (1971), 649–685.CrossRefGoogle Scholar
[5]Northcott, D. G.. A note on the coefficients of the abstract Hilbert function. J. London Math. Soc. 35 (1960), 209–214.CrossRefGoogle Scholar
[6]Rossi, M. E.. A bound on the reduction number of a primary ideal. Proc. Amer. Math. Soc. 128 (2000), 1325–1332.CrossRefGoogle Scholar
[7]Rossi, M. E. and Valla, G.. The Hilbert function of the Ratliff–Rush filtration. J. Pure Appl. Alg. 201 (2005), 25–41.CrossRefGoogle Scholar
[8]Rossi, M. E., Valla, G. and Vasconcelos, W. V.. Maximal Hilbert functions. Result. Math. 39 (2001), 99–114.CrossRefGoogle Scholar
[9]Sally, J. and Vasconcelos, W. V.. Stable rings. J. Pure Appl. Alg. 4 (1974), 319–336.CrossRefGoogle Scholar
[10]Singh, B.. Effect of a permisible blowing-up on the local Hilbert function. Inv. Math. 26 (1974), 201–212.CrossRefGoogle Scholar