Artin-Nagata properties and Cohen-Macaulay associated graded rings

 Access to full text

 Full (PDF)

1. 1 I.M. Aberbach, Local reduction numbers and Cohen-Macaulayness of associated graded rings, preprint, 1994. Zbl0918.13001MR1364345
2. 2 I.M. Aberbach and S. Huckaba, Reduction number bounds on analytic deviation two ideals and Cohen-Macaulayness of associated graded rings, Comm. Algebra23 (1995), 2003-2026. Zbl0831.13002MR1327119
3. 3 I.M. Aberbach, S. Huckaba and C. Huneke, Reduction numbers, Rees algebras, and Pfaffian ideals, J. Pure and Applied Algebra, to appear. Zbl0838.13003MR1350205
4. 4 I.M. Aberbach and C. Huneke, An improved Briançon-Skoda theorem with applications to the Cohen-Macaulayness of Rees algebras, Math. Ann.297 (1993), 343-369. Zbl0788.13001MR1241812
5. 5 I.M. Aberbach, C. Huneke and N.V. Trung, Reduction numbers, Briançon-Skoda theorems and depth of Rees algebras, preprint, 1993. Zbl0854.13003
6. 6 M. Artin and M. Nagata, Residual intersections in Cohen-Macaulay rings, J. Math. Kyoto Univ.12 (1972), 307-323. Zbl0263.14019MR301006
7. 7 L. Avramov and J. Herzog, The Koszul algebra of a codimension 2 embedding, Math. Z.175 (1980), 249-280. Zbl0461.14014MR602637
8. 8 D. Eisenbudand S. Goto, Linear free resolutions and minimal multiplicities, J. Algebra88 (1984), 89-133. Zbl0531.13015MR741934
9. 9 D. Eisenbud and C. Huneke, Cohen-Macaulay Rees algebras and their specializations, J. Algebra81 (1983), 202-224. Zbl0528.13024MR696134
10. 10 S. Goto and S. Huckaba, On graded rings associated to analytic deviation one ideals, Amer. J. Math.116 (1994), 905-919. Zbl0803.13002MR1287943
11. 11 S. Goto and Y. Nakamura, On the Gorensteinness of graded rings associated to ideals of analytic deviation one, Contemporary Mathematics159 (1994), 51-72. Zbl0816.13004MR1266179
12. 12 S. Goto and Y. Nakamura, Cohen-Macaulay Rees algebras of ideals having analytic deviation two, Tohoku Math. J.46 (1994), 573-586. Zbl0812.13003MR1301290
13. 13 S. Goto and Y. Nakamura, Gorenstein graded rings associated to ideals of analytic deviation two, preprint, 1993. Zbl0848.13005
14. 14 S. Goto, Y. Nakamura, and K. Nishida, Cohen-Macaulayness in graded rings associated to ideals, preprint, 1994. Zbl0878.13003MR1266179
15. 15 M. Herrmann, S. Ikeda and U. Orbanz, Equimultiplicity and Blowing-up, Springer Verlag, Berlin, 1988. Zbl0649.13011MR954831
16. 16 M. Herrmann, C. Huneke and J. Ribbe, On reduction exponents of ideals with Gorenstein formrings, preprint, 1993. Zbl0842.13001
17. 17 J. Herzog, A. Simis and W.V. Vasconcelos, Koszul homology and blowing-up rings, in Commutative Algebra, Proceedings, Trento1981 (S. Greco and G. Valla, Eds.), Lecture Notes in Pure and Applied Math.84, Marcel Dekker, New York, 1983, 79-169. Zbl0499.13002MR686942
18. 18 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. Algebra105 (1987), 285-302. Zbl0613.13007MR873664
19. 19 J. Herzog, W.V. Vasconcelos and R. Villarreal, Ideals with sliding depth, Nagoya Math. J.99 (1985), 159-172. Zbl0561.13014MR805087
20. 20 S. Huckaba and C. Huneke, Powers of ideals having small analytic deviation, American J. Math.114 (1992), 367-403. Zbl0758.13001MR1156570
21. 21 S. Huckaba and C. Huneke, Rees algebras of ideals having small analytic deviation, Trans. Amer. Math. Soc.339 (1993), 373-402. Zbl0813.13009MR1123455
22. 22 C. Huneke, Symbolic powers of prime ideals and special graded algebras, Comm. Algebra9 (1981), 339-366. Zbl0454.13003MR605026
23. 23 C. Huneke, The theory of d-sequences and powers of ideals, Adv. Math.46 (1982), 249-279. Zbl0505.13004MR683201
24. 24 C. Huneke, On the associated graded ring of an ideal, Illinois J. Math.26 (1982), 121-137. Zbl0479.13008MR638557
25. 25 C. Huneke, Linkage and Koszul homology of ideals, American J. Math.104 (1982), 1043-1062. Zbl0505.13003MR675309
26. 26 C. Huneke, Strongly Cohen-Macaulay schemes and residual intersections, Trans. Amer. Math. Soc.277 (1983), 739-763. Zbl0514.13011MR694386
27. 27 C. Huneke, Numerical invariants of liaison classes, Invent. Math.75 (1984), 301-325. Zbl0536.13005MR732549
28. 28 C. Huneke and B. Ulrich, Residual intersections, J. reine angew. Math.390 (1988), 1-20. Zbl0732.13004MR953673
29. 29 B. Johnston and D. Katz, Castelnuovo regularity and graded rings associated to an ideal, Proc. Amer. Math. Soc.123 (1995), 727-734. Zbl0826.13014MR1231300
30. 30 J. Lipman, Cohen-Macaulayness in graded algebras, Math. Research Letters1 (1994), 149-157. Zbl0844.13006MR1266753
31. 31 D.G. Northcott and D. Rees, Reductions of ideals in local rings, Math. Proc. Camb. Phil. Soc.50 (1954), 145-158. Zbl0057.02601MR59889
32. 32 A. Ooishi, Castelnuovo's regularity of graded rings and modules, Hiroshima Math. J.12 (1982), 627-644. Zbl0557.13007MR676563
33. 33 A. Simis, B. Ulrich and W.V. Vasconcelos, Cohen-Macaulay Rees algebras and degrees of polynomial relations, Math. Ann.301 (1995), 421-444. Zbl0819.13003MR1324518
34. 34 H. Srinivasan, A grade five cyclic Gorenstein module with no minimal algebra resolutions, preprint. Zbl0856.13011
35. 35 Z. Tang, Rees rings and associated graded rings of ideals having higher analytic deviation, Comm. Algebra22 (1994), 4855-4898. Zbl0803.13003MR1285714
36. 36 N.V. Trung, Reduction exponent and degree bound for the defining equations of graded rings, Proc. Amer. Math. Soc.101 (1987), 229-236. Zbl0641.13016MR902533
37. 37 N.V. Trung and S. Ikeda, When is the Rees algebra Cohen-Macaulay ?, Comm. Algebra17 (1989), 2893-2922. Zbl0696.13015MR1030601
38. 38 B. Ulrich, Artin-Nagata properties and reductions of ideals, Contemporary Mathematics159 (1994), 373-400. Zbl0821.13008MR1266194
39. 39 B. Ulrich and W.V. Vasconcelos, The equations of Rees algebras of ideals with linear presentation, Math. Z.214 (1993), 79-92. Zbl0789.13002MR1234599
40. 40 P. Valabrega and G. Valla, Form rings and regular sequences, Nagoya Math. J.72 (1978), 93-101. Zbl0362.13007MR514892
41. 41 W.V. Vasconcelos, Hilbert functions, analytic spread and Koszul homology, Contemporary Mathematics159 (1994), 401-422. Zbl0803.13012MR1266195