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Castelnuovo regularity and graded rings associated to an ideal


Authors: Bernard Johnston and Daniel Katz
Journal: Proc. Amer. Math. Soc. 123 (1995), 727-734
MSC: Primary 13A30; Secondary 13D45, 13H10
DOI: https://doi.org/10.1090/S0002-9939-1995-1231300-1
MathSciNet review: 1231300
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Abstract: We compare the Castelnuovo regularity defined with respect to different homogeneous ideals in a graded ring and use the result we obtain to prove a generalized Goto-Shimoda theorem for ideals of positive height in a Cohen-Macaulay local ring.


References [Enhancements On Off] (What's this?)

  • [AHT] I. Aberbach, C. Huneke, and N. V. Trung, Reduction numbers, Briançon-Skoda theorems and the depth of the Rees algebra, preprint.
  • [B] M. Brodmann, Einige Ergebnisse aus der lokalen Kohomologie Theorie und ihre Anwendung, Osnabrück. Schrift. Math. Reihe Math. Manuskr., Heft 5, Univ. Osnabrück, Osnabrück, 1983. MR 838084 (87j:14005)
  • [GH] S. Goto and S. Huckaba, On graded rings associated to analytic deviation one ideals, Amer. J. Math. (to appear). MR 1287943 (95h:13003)
  • [GHO] U. Grothe, M. Hermann, and U. Orbanz, Graded rings associated to equimultiple ideals, Math. Z. 186 (1984), 531-556. MR 744964 (86c:13019)
  • [GS] S. Goto and Y. Shimoda, On the Rees algebras of Cohen-Macaulay local rings, Lecture Notes in Pure and Appl. Math., vol. 68, Marcel Dekker, New York, 1979, pp. 201-231. MR 655805 (84a:13021)
  • [HIO] M. Hermann, S. Ikeda, and U. Orbanz, Equimultiplicity and blowing-up, Springer-Verlag, Berlin, 1988. MR 954831 (89g:13012)
  • [HH1] S. Huckaba and C. Huneke, Powers of ideals having small analytic deviation, Amer. J. Math. 114 (1992), 367-403. MR 1156570 (93g:13002)
  • [HH2] S. Huckaba and C. Huneke, Rees algebras of ideals having small analytic deviation, Trans. Amer. Math. Soc. 399 (1993), 373-402. MR 1123455 (93k:13008)
  • [H] C. Huneke, On the associated graded ring of an ideal, Illinois J. Math. 26 (1982), 212-137. MR 638557 (83d:13029)
  • [Mc] S. McAdam, Asymptotic prime divisors, Lecture Notes in Math., vol. 1023, Springer, Berlin, 1983. MR 722609 (85f:13018)
  • [NR] D. G. Northcott and D. Rees, Reductions of ideals in local rings, Math. Proc. Cambridge Philos. Soc. 50 (1952), 145-158. MR 0059889 (15:596a)
  • [SUV] A. Simis, B. Ulrich, and W. Vasconcelos, Cohen-Macaulay Rees algebras and degrees of polynomial relations, preprint. MR 1324518 (96a:13005)
  • [T] N. V. Trung, Reduction exponent and degree bound for the defining equations of graded rings, Proc. Amer. Math. Soc. 101 (1987), 229-236. MR 902533 (89i:13031)
  • [TI] N. V. Trung and S. Ikeda, When is the Rees ring Cohen-Macaulay?, Comm. Algebra 17 (1989), 2839-2922. MR 1030601 (91a:13009)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1231300-1
Article copyright: © Copyright 1995 American Mathematical Society

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