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
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by Ngô Viêt Trung

Proc. Amer. Math. Soc. 101 (1987), 229-236

DOI: https://doi.org/10.1090/S0002-9939-1987-0902533-1

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Abstract:

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

References

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 Mathematik, vol. 48, Teubner, Leipzig, 1982, pp. 77–87. MR 686461
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, DOI 10.1090/S0002-9939-1983-0718974-8
Peter Schenzel, Ngô Viêt Trung, and Nguyễn Tụ’ Cu’ò’ng, Verallgemeinerte Cohen-Macaulay-Moduln, Math. Nachr. 85 (1978), 57–73 (German). MR 517641, DOI 10.1002/mana.19780850106
David Eisenbud and Shiro Goto, Linear free resolutions and minimal multiplicity, J. Algebra 88 (1984), no. 1, 89–133. MR 741934, DOI 10.1016/0021-8693(84)90092-9
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
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, DOI 10.1007/BF01162779

Presentation of associated graded rings as quotient of polynomials

Craig Huneke, The theory of $d$-sequences and powers of ideals, Adv. in Math. 46 (1982), no. 3, 249–279. MR 683201, DOI 10.1016/0001-8708(82)90045-7
D. G. Northcott and D. Rees, Reductions of ideals in local rings, Proc. Cambridge Philos. Soc. 50 (1954), 145–158. MR 59889, DOI 10.1017/s0305004100029194
Akira Ooishi, Castelnuovo’s regularity of graded rings and modules, Hiroshima Math. J. 12 (1982), no. 3, 627–644. MR 676563
Judith D. Sally, Bounds for numbers of generators of Cohen-Macaulay ideals, Pacific J. Math. 63 (1976), no. 2, 517–520. MR 409453
Judith D. Sally, Tangent cones at Gorenstein singularities, Compositio Math. 40 (1980), no. 2, 167–175. MR 563540
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
Jürgen Stückrad and Wolfgang Vogel, Toward a theory of Buchsbaum singularities, Amer. J. Math. 100 (1978), no. 4, 727–746. MR 509072, DOI 10.2307/2373908
Ngô Viêt Trung, Absolutely superficial sequences, Math. Proc. Cambridge Philos. Soc. 93 (1983), no. 1, 35–47. MR 684272, DOI 10.1017/S0305004100060308
Ngô Việt Trung, Projections of one-dimensional Veronese varieties, Math. Nachr. 118 (1984), 47–67. MR 773610, DOI 10.1002/mana.19841180104
Paolo Valabrega and Giuseppe Valla, Form rings and regular sequences, Nagoya Math. J. 72 (1978), 93–101. MR 514892
Wolmer V. Vasconcelos, Ideals generated by $R$-sequences, J. Algebra 6 (1967), 309–316. MR 213345, DOI 10.1016/0021-8693(67)90086-5

Commutative algebra