Mathematische Annalen

, Volume 301, Issue 1, pp 421–444 | Cite as

Cohen-Macaulay Rees algebras and degrees of polynomial relations

  • Aron Simis
  • Bernd Ulrich
  • Wolmer V. Vasconcelos

Mathematics Subject Classification (1991)

13D40 13D45 13H15 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    I.M. Aberbach, S. Huckaba, C. Huneke, Reduction numbers, Rees algebras, and Pfaffian ideals. (Preprint 1993)Google Scholar
  2. 2.
    I.M. Aberbach, C. Huneke, An improved Briançon-Skoda theorem with the applications to the Cohen-Macaulayness of Rees algebras. Math. Ann. (to appear)Google Scholar
  3. 3.
    I.M. Aberbach, C. Huneke, N.V. Trung, Reduction numbers, Briançon-Skoda theorems, and the depth of Rees algebras. (Preprint 1993)Google Scholar
  4. 4.
    S. Abhyankar,Algebraic Geometry for Scientists and Engineers. Math. Surv. Monogr.95, Am. Math. Soc., Providence, RI 1990Google Scholar
  5. 5.
    M. Artin, M. Nagata, Residual intersections in Cohen-Macaulay rings. J. Math. Kyoto Univ.12 (1972), 307–323Google Scholar
  6. 6.
    L. Avramov, J. Herzog, The Koszul algebra of a codimension 2 embedding. Math. Z.175 (1980), 249–280Google Scholar
  7. 7.
    R.C. Cowsik, M.V. Nori, On the fibers of blowing up. J. Indian Math. Soc.40 (1976), 217–222Google Scholar
  8. 8.
    S. Goto, S. Huckaba, On graded rings associated to analytic deviation one ideals. Am. J. Math. (to appear)Google Scholar
  9. 9.
    S. Goto, Y. Nakamura, On the Gorensteinness of graded rings associated to ideals of analytic deviation one. (Preprint 1993)Google Scholar
  10. 10.
    S. Goto, Y. Shimoda, On the Rees algebras of Cohen-Macaulay local rings. Lect. Notes Pure Appl. Math.68, Marcel Dekker, New York, 1979, 201–231Google Scholar
  11. 11.
    S. Goto, K. Watanabe, On graded rings I. J. Math. Soc. Japan30 (1978), 179–213Google Scholar
  12. 12.
    U. Grothe, M. Herrmann, U. Orbanz, Graded rings associated to equimultiple ideals. Math. Z.186 (1984), 531–556Google Scholar
  13. 13.
    M. Herrmann, S. Ikeda, U. Orbanz, Equimultiplicity and Blowing up. Springer, Berlin-Heidelberg-New York 1988Google Scholar
  14. 14.
    J. Herzog, A. Simis, W.V. Vasconcelos, Koszul homology and blowing-up rings. In: Commutative Algebra, Proceedings: Trento 1981 (S. Greco and G. Valla, Eds.), Lect. Notes Pure Appl. Math.84, Marcel Dekker, New York, 1983, 79–169Google Scholar
  15. 15.
    J. Herzog, A. Simis, W.V. Vasconcelos, On the arithmetic and homology of algebras of linear type. Trans. Am. Math. Soc.283 (1984), 661–683Google Scholar
  16. 16.
    J. Herzog, A. Simis, W.V. Vasconcelos, On the canonical module of the Rees algebra and the associated graded ring of an ideal. J. Algebra105 (1987), 285–302Google Scholar
  17. 17.
    J. Herzog, W.V. Vasconcelos, R. Villarreal, Ideals with sliding depth. Nagoy Math. J.99 (1985), 159–172Google Scholar
  18. 18.
    M. Hochster, Properties of Noetherian rings stable under general grade reduction. Arch. Math.24 (1973), 393–396Google Scholar
  19. 19.
    S. Huckaba, Reduction numbers for ideals of higher analytic spread. Math. Proc. Camb. Philos. Soc.102 (1987), 49–57Google Scholar
  20. 20.
    S. Huckaba, C. Huneke, Rees algebras of ideals having small analytic deviation. Trans. Am. Math. Soc. (to appear)Google Scholar
  21. 21.
    C. Huneke, On the associated graded ring of an ideal. Ill. J. Math.26 (1982), 121–137Google Scholar
  22. 22.
    C. Huneke, Linkage and Koszul homology of ideals. Am. J. Math.104 (1982), 1043–1062Google Scholar
  23. 23.
    C. Huneke, M.E. Rossi, The dimension and components of symmetric algebras. J. Algebra98 (1986), 200–210Google Scholar
  24. 24.
    C. Huneke and B. Ulrich, Residual intersections. J. Reine Angew. Math.390 (1988), 1–20Google Scholar
  25. 25.
    S. Ikeda, N.V. Trung, When is the Rees algebra Cohen-Macaulay? Commun. Algebra17 (1989), 2893–2922Google Scholar
  26. 26.
    B. Johnston, D. Katz, Castelnuovo regularity and graded rings associated to an ideal. Proc. Am. Math. Soc. (to appear)Google Scholar
  27. 27.
    J. McKay, S. Wang, An inversion formula for two polynomials in two variables. J. Pure Appl. Algebra40 (1986), 245–257Google Scholar
  28. 28.
    S. Noh, W.V. Vasconcelos, TheS 2-closure of Rees algebras. Res. Math.23 (1993), 149–162Google Scholar
  29. 29.
    D.G. Northcott, D. Rees, Reductions of ideals in local rings. Proc. Camb. Philos. Soc.50 (1954), 145–158Google Scholar
  30. 30.
    C. Peskine, L. Szpiro, Liaison des variétés algébriques. Invent. Math.26 (1974), 271–302Google Scholar
  31. 31.
    B. Sturmfels, J.-T. Yu, Minimal polynomials and sparse resultants. (Preprint 1992)Google Scholar
  32. 32.
    Z. Tang, Rees rings and associated graded rings of ideals having higher analytic deviation. (Preprint 1993)Google Scholar
  33. 33.
    N.V. Trung, Reduction numbers,a-invariants and Rees algebras of ideals having small analytic deviation. (Preprint 1993)Google Scholar
  34. 34.
    B. Ulrich, Artin-Nagata properties and reductions of ideals. Contemp. Math. (to appear)Google Scholar
  35. 35.
    B. Ulrich, W.V. Vasconcelos, The equations of Rees algebras of ideals with linear presentation. Math. Z.214 (1993), 79–92Google Scholar
  36. 36.
    W.V. Vasconcelos, On the equations of Rees algebras. J. Reine Angew. Math.418 (1991), 189–218Google Scholar
  37. 37.
    W.V. Vasconcelos, Hilbert functions, analytic spread and Koszul homology. Contemp. Math. (to appear)Google Scholar
  38. 38.
    O. Zariski, Generalized weight properties of the resultant ofn+1 polynomials inn variables. Trans. Am. Math. Soc.41 (1937), 250–264Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Aron Simis
    • 1
  • Bernd Ulrich
    • 2
  • Wolmer V. Vasconcelos
    • 3
  1. 1.Instituto de MatemáticaUniversidade Federal da BahiaSalvadorBrazil
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA
  3. 3.Department of MathematicsRutgers UniversityNew BrunswickUSA

Personalised recommendations