Reduction numbers and multiplicities of multigraded structures

Journal of Algebra

Volumn 197, Issue 2, 1997, Pages 311-341

  Herrmann, Manfred ^a   Hyry, Eero ^a   Ribbe, Jürgen ^a   Tang, Zhongming ^a  

^a UNIVERSITY OF COLOGNE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031573417     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.1997.7128     Document Type: Article

References (29)

1. Bhattacharya P. B. The Hilbert function of two ideals. Proc. Camb. Phil. Soc. 53:1957;568-575.
2. Bruns W., Herzog J. Cohen-Macaulay Rings. 1993;Cambridge Univ. Press, Cambridge.
3. Goto S., Huckaba S. On graded rings associated with analytic deviation one ideals. Amer. J. Math. 116:1994;905-919.
4. Goto S., Watanabe K. On graded rings I. J. Math. Soc. Japan. 30:1978;179-213.
5. Goto S., Watanabe K. On graded rings II. Tokyo J. Math. 1:1978;237-260.
6. Hoa L. T. Reduction numbers and Rees algebras of powers of an ideal. Proc. Amer. Math. Soc. 119:1994;415-422.
7. L. T. Hoa, Reduction numbers of equimultiple ideals.
8. Herrmann M., Hyry E., Ribbe J. On the Cohen-Macaulay and Gorenstein properties of multi-Rees algebras. Manuscripta. Math. 79:1993;343-377.
9. Herrmann M., Hyry E., Ribbe J. On multi-Rees algebras. Math. Ann. 301:1995;249-279.
10. Herrmann M., Ikeda S., Orbanz U. Equimultiplicity and Blowing Up. 1988;Springer-Verlag, Berlin/Heidelberg/New York.
11. Hermann M., Ribbe J., Zarzuela S. On the Gorenstein property of Rees and form rings of powers of ideals. Trans. Amer. Math. Soc. 342:1994;631-643.
12. D. Katz, S. Mandal, J. Verma, 1994, Hilbert functions of bigraded algebras, Proceedings of the First ICTP Workshop on Commutative Algebra 1992, World Scientific, London.
13. Kleiman S., Thorup A. A geometric theory of the Buchsbaum-Rim multiplicity. J. Algebra. 167:1994;168-231.
14. Katz D., Verma J. K. Extended Rees algebras and mixed multiplicities. Math. Z. 202:1989;111-128.
15. Lipman J. Cohen-Macaulayness in graded algebras. Math. Res. Lett. 1:1994;149-157.
16. Matsumura N. Commutative Ring Theory. 1986;Cambridge Univ. Press, Cambridge.
17. Marley T. The reduction number of an ideal and the local cohomology of the associated graded ring. Proc. Amer. Math. Soc. 117:1993;335-341.
18. Rees D. Generalizations of reductions and mixed multiplicities. J. London Math. Soc. (2). 29:1984;397-414.
19. Sally J. On the number of generators of powers of an ideal. Proc. Amer. Math. Soc. 53:1975;24-26.
20. Sally J. On the associated graded ring of a local Cohen-Macaulay ring. J. Math Kyoto. 17:1977;19-21.
21. I. Swanson, 1992, Tight Closure, Joint Reductions, and Mixed Multiplicities, Purdue University.
22. Teissier B. Cycles èvanescents, sections planes, et conditions de Whitney, Singularités à Cargése 1972. Astérisque. 7-8:1973;285-362.
23. Trung N. V., Ikeda S. When is the Rees algebra Cohen-Macaulay? Commun. Alg. 17:1989;2893-2922.
24. N. V. Trung, 1994, Reduction numbers, a-invariants and Rees algebras of ideals having small analytic deviation, Proceedings, first ICTP Workshop on Commutative Algebra 1992, World Scientific, London.
25. Valabrega P., Valla G. Form rings and regular sequences. Nagoya Math. J. 72:1978;93-101.
26. Verma J. K. Rees algebras with minimal multilicity. Commun. Algebra. 17:1989;2999-3024.
27. Verma J. K. Joint reductions of complete ideals. Nagoya Math. J. 118:1990;155-163.
28. Verma J. K. Joint reductions and Rees algebras. Math. Proc. Camb. Phil. Soc. 109:1991;335-343.
29. Verma J. K. Multigraded Rees algebras and mixed multiplicities. Journal of Pure and Applied Algebra. 77:1992;219-228.