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On the Gorenstein property of Rees and form rings of powers of ideals

Authors: M. Herrmann, J. Ribbe and S. Zarzuela
Journal: Trans. Amer. Math. Soc. 342 (1994), 631-643
MSC: Primary 13A30; Secondary 13H10
MathSciNet review: 1159193
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Abstract: In this paper we determine the exponents n for which the Rees ring $ R({I^n})$ and the form ring $ {\text{gr}}_{A}({I^n})$ are Gorenstein rings, where I is a strongly Cohen-Macaulay ideal of linear type (including complete and almost complete intersections) or an $ \mathfrak{m}$-primary ideal in a local ring A with maximal ideal $ \mathfrak{m}$.

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  • [1] S. Goto and Y. Shimoda, On the Rees algebras of Cohen-Macaulay rings, Commutative Algebra: Analytical Methods (R. N. Draper, ed.), Lecture Notes in Pure and Appl. Math., vol. 68, Dekker, New York and Basel, 1982, pp. 201-231. MR 655805 (84a:13021)
  • [2] M. Herrmann and S. Ikeda, On the Gorenstein property of Rees algebras, Manuscripta Math. 59 (1987), 471-490. MR 915998 (88i:13030)
  • [3] M. Herrmann, S. Ikeda, and U. Orbanz, Equimultiplicity and blowing up, Springer-Verlag, Berlin and Heidelberg, 1988. MR 954831 (89g:13012)
  • [4] J. Herzog, A. Simis, and W. V. Vasconcelos, Koszul homology and blowing up rings, Commutative Algebra, Proc. Trento Conf. (S. Greco and G. Valla, eds.), Lecture Notes in Pure and Appl. Math., vol 84, Dekker, New York and Basel 1983, pp. 79-169. MR 686942 (84k:13015)
  • [5] -, Approximation complexes of blowing up rings, J. Algebra 74 (1982), 466-493. MR 647249 (83h:13023)
  • [6] -, Approximation complexes of blowing up rings. II, J. Algebra 82 (1983), 53-83. MR 701036 (85b:13015)
  • [7] -, On the canonical module of the Rees algebra and the associated graded ring of an ideal, J. Algebra 105 (1987), 285-302. MR 873664 (87m:13029)
  • [8] S. Ikeda, On the Gorensteinness of Rees algebras over local rings, Nagoya Math. J. 102 (1986), 135-154. MR 846135 (87j:13031)
  • [9] T. Marley, The coefficients of the Hilbert polynomial and the reduction number of an ideal, J. London Math. Soc. (2) 40 (1989), 1-8. MR 1028910 (90m:13026)
  • [10] A. Ooishi, Stable ideals in Gorenstein local rings, J. Pure Appl. Algebra 69 (1990), 185-191. MR 1086560 (92b:13032)
  • [11] -, On the Gorenstein property of the associated graded ring and the Rees algebra of an ideal, preprint, 1990.
  • [12] J. Ribbe, Thesis, Universität zu Köln, 1991.
  • [13] J. Sally, Tangent cones at Gorenstein singularities, Compositio Math. (2) 40 (1980), 167-175. MR 563540 (81e:14004)
  • [14] P. Schenzel, Dualisierende Komplexe in der lokalen Algebra und Buchsbaum-Ringe, Lecture Notes in Math., vol. 907, Springer-Verlag, 1982. MR 654151 (83i:13013)
  • [15] N. V. Trung and S. Ikeda, When is the Rees algebra Cohen-Macaulay?, Comm. Algebra 17 (1989), 2893-2922. MR 1030601 (91a:13009)
  • [16] A. Lascu and M. Fiorentini, Linkage among subcanonical and quasicomplete intersection projective schemes, preprint, 1991.

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