Reduction exponent and degree bound for the defining equations of graded rings

Trung, Ngô Viêt

doi:10.1090/S0002-9939-1987-0902533-1

Reduction exponent and degree bound for the defining equations of graded rings

Author: Ngô Viêt Trung
Journal: Proc. Amer. Math. Soc. 101 (1987), 229-236
MSC: Primary 13H10; Secondary 13H15, 14B15
DOI: https://doi.org/10.1090/S0002-9939-1987-0902533-1
MathSciNet review: 902533
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The paper gives upper degree bounds for the defining equations of certain graded rings in terms of the reduction exponent and the multiplicity.

[1] Rüdiger Achilles and Peter Schenzel, A degree bound for the defining equations of one-dimensional tangent cones, Seminar D. Eisenbud/B. Singh/W. Vogel, Vol. 2, Teubner-Texte zur Math., vol. 48, Teubner, Leipzig, 1982, pp. 77–87. MR 686461
[2] Young-Hyun Cho, Presentation of associated graded rings of Cohen-Macaulay local rings, Proc. Amer. Math. Soc. 89 (1983), no. 4, 569–573. MR 718974, https://doi.org/10.1090/S0002-9939-1983-0718974-8
[3] Peter Schenzel, Ngô Viêt Trung, and Nguyá»…n Tá»¥’ Cu’ò’ng, Verallgemeinerte Cohen-Macaulay-Moduln, Math. Nachr. 85 (1978), 57–73 (German). MR 517641, https://doi.org/10.1002/mana.19780850106
[4] David Eisenbud and Shiro Goto, Linear free resolutions and minimal multiplicity, J. Algebra 88 (1984), no. 1, 89–133. MR 741934, https://doi.org/10.1016/0021-8693(84)90092-9
[5] 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
[6] U. Grothe, M. Herrmann, and U. Orbanz, Graded Cohen-Macaulay rings associated to equimultiple ideals, Math. Z. 186 (1984), no. 4, 531–556. MR 744964, https://doi.org/10.1007/BF01162779
[7] Y. H. Hong, Presentation of associated graded rings as quotient of polynomials, Preprint, North-western University, Evanston, Ill., 1981.
[8] Craig Huneke, The theory of 𝑑-sequences and powers of ideals, Adv. in Math. 46 (1982), no. 3, 249–279. MR 683201, https://doi.org/10.1016/0001-8708(82)90045-7
[9] D. G. Northcott and D. Rees, Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50 (1954), 145–158. MR 0059889
[10] Akira Ooishi, Castelnuovo’s regularity of graded rings and modules, Hiroshima Math. J. 12 (1982), no. 3, 627–644. MR 676563
[11] Judith D. Sally, Bounds for numbers of generators of Cohen-Macaulay ideals, Pacific J. Math. 63 (1976), no. 2, 517–520. MR 0409453
[12] Judith D. Sally, Tangent cones at Gorenstein singularities, Compositio Math. 40 (1980), no. 2, 167–175. MR 563540
[13] Judith D. Sally, Reductions, local cohomology and Hilbert functions of local rings, Commutative algebra: Durham 1981 (Durham, 1981) London Math. Soc. Lecture Note Ser., vol. 72, Cambridge Univ. Press, Cambridge-New York, 1982, pp. 231–241. MR 693638
[14] Jürgen Stückrad and Wolfgang Vogel, Toward a theory of Buchsbaum singularities, Amer. J. Math. 100 (1978), no. 4, 727–746. MR 509072, https://doi.org/10.2307/2373908
[15] Ngô Viêt Trung, Absolutely superficial sequences, Math. Proc. Cambridge Philos. Soc. 93 (1983), no. 1, 35–47. MR 684272, https://doi.org/10.1017/S0305004100060308
[16] Ngô Viá»‡t Trung, Projections of one-dimensional Veronese varieties, Math. Nachr. 118 (1984), 47–67. MR 773610, https://doi.org/10.1002/mana.19841180104
[17] Paolo Valabrega and Giuseppe Valla, Form rings and regular sequences, Nagoya Math. J. 72 (1978), 93–101. MR 514892
[18] Wolmer V. Vasconcelos, Ideals generated by 𝑅-sequences, J. Algebra 6 (1967), 309–316. MR 0213345, https://doi.org/10.1016/0021-8693(67)90086-5
[19] O. Zariski and P. Samuel, Commutative algebra. II, Springer-Verlag, Berlin and New York, 1975.