On the cohen-macaulayness of multi-rees algebras and rees algebras of powers of ideals

Journal of the Mathematical Society of Japan

Volumn 50, Issue 2, 1998, Pages 451-467

  Korb, Thomas ^a   Nakamura, Yukio ^b  

^a UNIVERSITY OF COLOGNE   (Germany)

^b TOKYO METROPOLITAN UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039401964     PISSN: 00255645     EISSN: 18811167     Source Type: Journal    
DOI: 10.2969/jmsj/05020451     Document Type: Article

References (32)

1. S. Goto, On Buchsbaum rings. J. of Algebra 67, No. 2 (1980), 272-279.
2. S. Goto, On the associated graded rings of parameter ideals in Buchsbaum rings. J. of Algebra, 85, No. 2 (1983), 490-534.
3. S. Goto and S. Huckaba, On graded rings associated to analytic deviation one ideals. Amer. J. Math. 116 (1994), 905-919.
4. S. Goto and K. Nishida, The Cohen-Macaulay and Gorenstein Rees algebras associated to filtrations. Mem. Amer. Math. Soc. 526 (1994).
5. S. Goto and K. Watanabe, On graded rings, I. J. Math. Soc. Japan 30 (1978), 179-213.
6. M. Herrmann, E. Hyry and T. Korb, Filter-regularity and Cohen-Macaulay multi-graded Rees algebras, (in preparation).
7. M. Herrmann, E. Hyry and J. Ribbe, On the Cohen-Macaulay and Gorenstein properties of multi-Rees algebras. Manus. Mat. 79 (1993), 343-377.
8. M. Herrmann, E. Hyry and J. Ribbe, On multi-Rees algebras (with an appendix by N. V. Trung). (To appear in Math. Ann.).
9. M. Herrmann, E. Hyry, J. Ribbe and Z. Tang, Reduction numbers and multiplicities of multigraded structures, (preprint).
10. M. Herrmann, S. Ikeda, and U. Orbanz, Equimultiplicity and Blowing Up (with an appendix by B. Moonen). Springer-Verlag, Berlin-Heidelberg-New York (1988).
11. M. Herrmann, J. Ribbe and P. Schenzel, On the Gorenstein property of form rings. Math. Z. 213 (1993), 301-309.
12. M. Herrmann, J. Ribbe and S. Zarzuela, On the Gorenstein property of Rees and form rings of power of ideals. Trans. Amer. Math. Soc. 342, No. 2 (1994), 631-643.
13. L. T. Hoa, Reduction numbers and Rees algebras of powers of an ideal. Proc. of the AMS 119, No. 2 (1993), 415-422.
14. L. T. Hoa, Reduction numbers of equimultiple ideals, (preprint).
15. L. T. Hoa and S. Zarzuela, Reduction number and a-invariant of good filtrations. (preprint).
16. S. Huckaba and T. Marley, Depth formulas of certain graded rings associated to an ideal. Nagoya Math. J. 133 (1994), 57-69.
17. C. Huneke, On the associated graded ring of an ideal. Illinois J. Math. 26, No. 1 (1982), 121-137.
18. S. Ikeda, On the Gorensteinness of Rees algebras over local rings. Nagoya Math. J. 102 (1986), 135-154.
19. S. Itoh, Integral closure of ideals generated by regular sequences. J. of Algebra 117 (1988), 390-401.
20. T. Korb, On a-invariants, filter-regularity and the Cohen-Macaulayness of graded algebras. Thesis (1995), University of Cologne.
21. T. Marley, The reduction number of an ideal and the local cohomology of the associated graded ring. Proc. of the AMS 117, No. 2 (1993), 335-341.
22. M. Nagata, Local rings. Interscience (1962).
23. D. G. Northcott and D. Rees, Reductions of ideals in local rings. Proc. Camb. Phil. Soc. 50 (1954), 145-158.
24. A. Ooishi, On the Gorenstein property of the associated graded ring and the Rees algebra of an ideal. J. of Algebra 155 (1993), 397-414.
25. D. Rees, Generalizations of reductions and mixed multiplicities. J. London Math. Soc. (2) 29 (1984), 397-414.
26. J. D. Sally, On the number of generators of powers of an ideal. Proc. of the AMS. 53 (1975), 24-26.
27. J. Stückrad and W. Vogel, Toward a theory of Buchsbaum singularities. Amer. J. Math. 100 (1978), 727-746.
28. B. Teissier, Cycles évanescents, sections planes et conditions de Whitney. Singularitiés à Cargese 1972, Astérisque 7-8 (1973), 285-362.
29. N. V. Trung, Reduction exponent and degree bound for the defining equations of graded rings. Proc. of the AMS 101, No. 2 (1987), 229-236.
30. N. V. Trung and S. Ikeda, When is the Rees algebra Cohen-Macaulay? Communications in Algebra 17 [12] (1989), 2893-2922.
31. P. Valabrega and G. Valla, Form rings and regular sequences. Nagoya Math. J. 72 (1978), 93101.
32. J. K. Verma, Joint reductions and Rees algebras. Math. Proc. Camb. Phil. Soc. 109 (1991), 335-342.