Mathematische Zeitschrift

, Volume 186, Issue 4, pp 531–556

Graded Cohen-Macaulay rings associated to equimultiple ideals

  • U. Grothe
  • M. Herrmann
  • U. Orbanz


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abhyankar, S.S.: Local rings of high embedding dimension, Amer. J. Math.89, 1073–1077 (1967)Google Scholar
  2. 2.
    Altman, A., Kleiman, S.: Introduction to Grothendieck duality. Lecture Notes in Math.146. Berlin-Heidelberg-New York: Springer 1970Google Scholar
  3. 3.
    Dade, E.C.: Multiplicity and monoidal transformations. Thesis Princeton 1960 (unpublished)Google Scholar
  4. 4.
    Goto, S., Shimoda, Y.: On Rees algebras over Buchsbaum rings. J. Math. Kyoto Univ.20, 691–708 (1980)Google Scholar
  5. 5.
    Goto, S., Shimoda, Y.: On the Rees algebras of Cohen-Macaulay local rings. In: Commutative Algebra: Analytic Methods (ed. R. Draper) Lecture Notes in Pure and Applied Mathematics68, New York-Basel: Dekker 1981Google Scholar
  6. 6.
    Hartshorne, R.: Complete intersections and connectedness. Amer. J. Math.,84, 497–508 (1962)Google Scholar
  7. 7.
    Herrmann, M., Ikeda, S.: Remarks on lifting of Cohen-Macaulay property. To appear in Nagoya Math. J.92, 121–132 (1983)Google Scholar
  8. 8.
    Herrmann, M., Orbanz, U.: Faserdimensionen von Aufblasungen lokaler Ringe und Äquimultiplizität. J. Math. Kyoto Univ.20, 651–659 (1980)Google Scholar
  9. 9.
    Herrmann, M., Orbanz, U.: Normale Flachheit und Äquimultiplizität für vollständige Durchschnitte. J. Algebra70, 437–451 (1981)Google Scholar
  10. 10.
    Herrmann, M., Orbanz, U.: between equimultiplicity and normal flatness. In: Algebraic Geometry. Proceedings La Rabida 1981 (ed. Aroca/Buchweitz/Giusti/Merle), pp. 200–232. Lecture Notes in Mathematics961. Berlin-Heidelberg-New York: Springer 1982Google Scholar
  11. 11.
    Herrmann, M., Orbanz, U.: On equimultiplicity. Math. Proc. Camb. Phil. Soc.91, 207–213 (1982)Google Scholar
  12. 12.
    Herrmann, M., Schmidt, R., Vogel, W.: Theorie der normalen Flachheit. Teubner Texte zur Mathematik. Leipzig: Teubner 1977Google Scholar
  13. 13.
    Herzog, J., Simis, A., Vasconselos, W.V.: Koszul homology and blowing-up rings. In: Commutative Algebra, Proceedings of the Trento Conference (ed. Greco/Valla), pp. 79–169. Lecture Notes in Pure and Applied Math.84, New York-Basel: Dekker 1983Google Scholar
  14. 14.
    Huneke, C.: On the associated graded ring of an ideal. Illinois J. Math.26, 121–137 (1982)Google Scholar
  15. 15.
    Huneke, C.: A remark concerning multiplicities. Proc. Amer. Math. Soc.85, 331–332 (1982)Google Scholar
  16. 16.
    Ikeda, S.: The Cohen-Macaulayness of the Rees algebras of local rings. Nagoya Math. J.89, 47–63 (1983)Google Scholar
  17. 17.
    Lipman, J.: Equimultiplicity, reduction and blowing up. In: Commutative Algebra: Analytic Methods (ed. R. Draper). Lecture Notes in Pure and Applied Mathematics68, New York-Basel: Dekker 1981Google Scholar
  18. 18.
    Matijevic, J., Roberts, P.: A conjecture of Nagata on graded Cohen-Macaulay rings. J. Math. Kyoto Univ.14, 125–128 (1974)Google Scholar
  19. 19.
    Matsumura, H.: Commutative Algebra. New York: Benjamin 1970Google Scholar
  20. 20.
    Nagata, M.: Local rings. New York-London-Toronto: Wiley 1962Google Scholar
  21. 21.
    Northcott, D.G.: Lessons on rings, modules, and multiplicities. Cambridge: Cambridge University Press 1968Google Scholar
  22. 22.
    Orbanz, U.: Multiplicities and Hilbert functions under blowing up. Manuscripta Math.36, 179–186 (1981)Google Scholar
  23. 23.
    Orbanz, U., Robbiano, L.: Projective normal flatness and Hilbert functions. To appear in Trans. Amer. Math. Soc. 1984Google Scholar
  24. 24.
    Ratliff, L.J.: On quasi-unmixed local domains, the altitude formula, and the chain condition for prime ideals II. Amer. J. Math.92, 99–144 (1970)Google Scholar
  25. 25.
    Rees, D.: Valuations associated with ideals (II). J. London Math. Soc.31, 221–227 (1956)Google Scholar
  26. 26.
    Rees, D.:a-transforms of local rings and a theorem on multiplicities of ideals. Math. Proc. Camb. Phil. Soc.57, 8–17 (1961)Google Scholar
  27. 27.
    Robbiano, L.: Remarks on blowing up divisorial ideals, Manuscripta Math.30 (1980)Google Scholar
  28. 28.
    Robbiano, L.: On normal flatness and some related topics. In: Commutative Algebra, Proc. of the Trento Conference (ed. Greco/Valla). Lecture Notes in Pure and Applied Mathematics84, pp. 235–251. New York-Basel: Dekker 1983Google Scholar
  29. 29.
    Sally, J.: Numbers of generators of ideals in local rings. New York: Dekker 1978Google Scholar
  30. 30.
    Schenzel, P., Ngo viet Trung, Nguyen tu Cuong, Verallgemeinerte Cohen-Macaulay-Moduln. Math. Nachr.85, 57–73 (1978)Google Scholar
  31. 31.
    Schmidt, R.: Normale Flachheit als Spezialfall der Cohen-Macaulay-Eigenschaft von Graduierungen. Dissertation Berlin 1976Google Scholar
  32. 32.
    Valabrega, P., Valla, G.: Form rings and regular sequences. Nagoya Math. J.72, 93–101 (1978)Google Scholar
  33. 33.
    Valla, G.: Certain graded algebras are always Cohen-Macaulay. J. Algebra42, 537–548 (1976)Google Scholar
  34. 34.
    Valla, G.: On form rings which are Cohen-Macaulay, J. Algebra58, 247–250 (1979)Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • U. Grothe
    • 1
  • M. Herrmann
    • 1
  • U. Orbanz
    • 1
  1. 1.Mathematisches InstitutUniversität zu KölnKöln 41Federal Republic of Germany

Personalised recommendations