Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-18T03:51:03.449Z Has data issue: false hasContentIssue false
  • English
  • Français

On reduction exponents of ideals with Gorenstein formring*

Published online by Cambridge University Press:  20 January 2009

M. Herrmann ,
C. Huneke  and
J. Ribbe
M. Herrmann
Affiliation:
Mathematisches Institut der Univ. zu Koeln, Weyertal 86-90, D-50931 Koeln, Germany E-mail address: herrmann@mi.uni-koeln.de
C. Huneke
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN, USA E-mail address: huneke@math.purdue.edu
J. Ribbe
Affiliation:
Mathematisches Institut der Univ. zu Koeln, Weyertal 86-90, D-50931 Koeln, Germany E-mail address: ribbe@mi.uni-koeln.de
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper studies questions connected with when the Rees algebra of an ideal or the formring of an ideal is Gorenstein. The main results are for ideals of small analytic deviation, and for m-primary ideals of a regular local ring (R, m). The general point proved is that the Gorenstein property forces (and is sometimes equivalent to) lowering the reduction number of the ideal by one from the value predicted if one only assumes the Rees algebra or formring is Cohen–Macaulay.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 3 , October 1995 , pp. 449 - 463
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Aberbach, I. M. and Huneke, C., An improved Briançon-Skoda theorem with applications to the Cohen-Macaulayness of Rees algebras, Math. Ann. 297 (1993), 343–369.CrossRefGoogle Scholar
2.Evans, E. G. and Griffith, P., Syzygies (London Math. Soc. Lecture Note Senes 103, Cambridge University Press, Cambridge, 1985).CrossRefGoogle Scholar
3.Goto, S. and Huckaba, S., On graded rings associated to analytic deviation one ideals, Amer. J. Math. 116 (1994), 905–919.CrossRefGoogle Scholar
4.Goto, S. and Nakamura, Y., On the Gorensteinness of graded rings associated to ideals of analytic deviation one, (1992), preprint.Google Scholar
5.Goto, S. and Nakamura, Y., Gorenstein graded rings associated to ideals of analytic deviation two, (1993), preprint.CrossRefGoogle Scholar
6.Herrmann, M., Ikeda, S. and Orbanz, U., Equimultiplicity and Blowing Up (Springer-Verlag, Berlin-Heidelberg, 1988).CrossRefGoogle Scholar
7.Herzog, J., Simis, A. and Vasconcelos, W. V., Koszul homology and blowing up rings (Lecture Notes in Pure and Appl. Math. 84, Marcel Dekker, New York 1983), 79–169.Google Scholar
8.Hermmann, M., Ribbe, J. and Schenzel, P., On the Gorenstein property of form rings, Math. Z. 213 (1993), 301–309.CrossRefGoogle Scholar
9.Hermmann, M., Ribbe, J. and Zarzuela, S., On the Gorenstein property of Rees and form rings of powers of ideals, Trans. Amer. Math. Soc., to appear.Google Scholar
10.Huckaba, S. and Huneke, C., Powers of ideal having small analytic deviation, Amer. J. Math. 114 (1992), 367–403.CrossRefGoogle Scholar
11.Huckaba, S. and Huneke, C., Rees algebras of ideals having small analytic deviation, Trans. Amer. Math. Soc. 339 (1993), 373–402.CrossRefGoogle Scholar
12.Huneke, C., Linkage and the Koszul homology of ideals, Amer. J. Math. 104 (1982), 1043–1062.CrossRefGoogle Scholar
13.Lipman, J., Adjoint of ideals in regular local rings, Math. Res. Letter. 1 (1994), 1–17.Google Scholar
14.Mcadam, S., Finite coverings of ideals, in Ring Theory (Proc. of the Oklahoma Conference, Lecture Notes in Pure and Appl. Math., Marcel Dekker 7 1974), 163–171.Google Scholar
15.Noh, S. and Vasconcelos, W. V., The S2-closure of a Rees algebra, Results in Math. 23 (1993), 149–162.CrossRefGoogle Scholar
16.Raghavan, K. N., Uniform annihilation of local cohomology and powers of ideals generated by Quadratic sequences (Thesis, Purdue 1991).Google Scholar