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

Herrmann, M.; Ribbe, J.; Zarzuela, S.

doi:10.1090/S0002-9947-1994-1159193-5

On the Gorenstein property of Rees and form rings of powers of ideals
HTML articles powered by AMS MathViewer

by M. Herrmann, J. Ribbe and S. Zarzuela PDF

Trans. Amer. Math. Soc. 342 (1994), 631-643 Request permission

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 $\mathfrak {m}$.

References

Shiro Goto and Yasuhiro Shimoda, On the Rees algebras of Cohen-Macaulay local rings, Commutative algebra (Fairfax, Va., 1979) Lecture Notes in Pure and Appl. Math., vol. 68, Dekker, New York, 1982, pp. 201–231. MR 655805
Manfred Herrmann and Shin Ikeda, On the Gorenstein property of Rees algebras, Manuscripta Math. 59 (1987), no. 4, 471–490. MR 915998, DOI 10.1007/BF01170849
M. Herrmann, S. Ikeda, and U. Orbanz, Equimultiplicity and blowing up, Springer-Verlag, Berlin, 1988. An algebraic study; With an appendix by B. Moonen. MR 954831, DOI 10.1007/978-3-642-61349-4
J. Herzog, A. Simis, and W. V. Vasconcelos, Koszul homology and blowing-up rings, Commutative algebra (Trento, 1981) Lecture Notes in Pure and Appl. Math., vol. 84, Dekker, New York, 1983, pp. 79–169. MR 686942
J. Herzog, A. Simis, and W. V. Vasconcelos, Approximation complexes of blowing-up rings, J. Algebra 74 (1982), no. 2, 466–493. MR 647249, DOI 10.1016/0021-8693(82)90034-5
J. Herzog, A. Simis, and W. V. Vasconcelos, Approximation complexes of blowing-up rings. II, J. Algebra 82 (1983), no. 1, 53–83. MR 701036, DOI 10.1016/0021-8693(83)90173-4
J. Herzog, A. Simis, and W. V. Vasconcelos, On the canonical module of the Rees algebra and the associated graded ring of an ideal, J. Algebra 105 (1987), no. 2, 285–302. MR 873664, DOI 10.1016/0021-8693(87)90194-3
Shin Ikeda, On the Gorensteinness of Rees algebras over local rings, Nagoya Math. J. 102 (1986), 135–154. MR 846135, DOI 10.1017/S0027763000000489
Thomas Marley, The coefficients of the Hilbert polynomial and the reduction number of an ideal, J. London Math. Soc. (2) 40 (1989), no. 1, 1–8. MR 1028910, DOI 10.1112/jlms/s2-40.1.1
Akira Ooishi, Stable ideals in Gorenstein local rings, J. Pure Appl. Algebra 69 (1990), no. 2, 185–191. MR 1086560, DOI 10.1016/0022-4049(90)90042-G

On the Gorenstein property of the associated graded ring and the Rees algebra of an ideal

Universität zu Köln

Judith D. Sally, Tangent cones at Gorenstein singularities, Compositio Math. 40 (1980), no. 2, 167–175. MR 563540
Peter Schenzel, Dualisierende Komplexe in der lokalen Algebra und Buchsbaum-Ringe, Lecture Notes in Mathematics, vol. 907, Springer-Verlag, Berlin-New York, 1982 (German). With an English summary. MR 654151, DOI 10.1007/BFb0094123
Ngô Việt Trung and Shin Ikeda, When is the Rees algebra Cohen-Macaulay?, Comm. Algebra 17 (1989), no. 12, 2893–2922. MR 1030601, DOI 10.1080/00927878908823885

Linkage among subcanonical and quasicomplete intersection projective schemes